{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":51274,"title":"Solve a nonlinear difference equation","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 95.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.875px; transform-origin: 407px 47.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.25px; text-align: left; transform-origin: 384px 22.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.967px 7.91667px; transform-origin: 102.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the difference equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_{n+1} = a_n^p\" style=\"width: 60.5px; height: 22px;\" width=\"60.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 7.91667px; transform-origin: 48.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the initial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAABwElEQVRoge2YUbGDMBBFjwccYKAGUFAFOMABDmrhaaiEeqgFNGCB95HsZMsLIeG1hU73zGT6kbAkl5vdpGAYhmEYxudTAWeg9+2873SORw+MwA/Q4AS6+2Zi4YSZ/K+mwgk38eVCnXEiTDhR5rS+b1jo/woGnAi3hf6KIOLlXZM6EtpFfWLcneCmr0Ny0VrO0eNOJS84+cA6eIXbw59SPm/kLb5X47q1oN0s8IQTBZwo46yvRKiacD75T2sK3qnnmivSvAIuInt0JLhnIJwvtiS6ZjbprW31Syv0c3ViXKfGXXODS0W44hany6NebMlXfZaTSnKGzHNcGafXlCVSzeNXEwcJYk1x2ZHRIqWc1FIokn5g4K+9ryXBdkbn0KfmJBFh6QC2JTfsxUuqGwT1x0hgvXdT9o2xR3W7kJc/c8cBjyLEbCfBtpxM96huuhKnnhPHZeVZrWjMnnI0kNJf4qY9qhu84O6WusPoqtf44DfKJ/1uxE1LFa6lwEVa0dhlUB+4apygbWTcEUn9nyROy7o96NIfS166/1Oqm0ZSyfyfyZGC61VD2PdLdL6/tLIdhZpwQS+tlIZhGIZhGIZRxi8Ks/qCh9x2gAAAAABJRU5ErkJggg==\" alt=\"n = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.91667px; transform-origin: 22.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 7.91667px; transform-origin: 28.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAkCAYAAAAjMNwcAAAB10lEQVRoge2Z67GCMBBGTw90YAM2QAVUQAd2QAe0QA2UQA+2YA20oD82e4ne8AgwEnXPzM44E4nJx74SwTAMwzAMI8QZuACVs/zY5aTLCeiAe8CuiJCGIwN6BnE64MazaDdMtD9aRLBXQXJEQBWtffO6kuSEiDHmPTp+R0TN3rSuZKmAeuY7LYNoPx+WJeJFU1RsECxDYrtwEzXOcD9cI0mzc+Pf4MIqWL/mYRXMd9PaTXpznxueS3KMaNUOVq7Z2AS617nQnSRnEKXjfwXxe5oiYt5QHxRre1czbTnmQncSP65DC/THY97MHh4W84LmKJE9VFsn0v6kJ6z8WsFSIkPSTMfGXJwx7/4160IyJRpEsM2Fq2AQYyzB+h3yptg/iJLx6IlGq+BY5+t3x7EJOIUquatYMBxMl4RjbKN3dJXcXSzfey4j41qG11SWI6tkzrxYJyI9WMvsmPdo7vq0k/0ZEWtK7AzZX9QL8Tv81/ylua15fShxVKye4VgXsh5JR1FouPntQoEof+XzrnRVrKX5MSrNnL0HayQ8tSp9YusAwx6WWlRPtuma4xfRA/Wqa45fY8lxyPDwj0Oh/stwZIhY/t9OLVINv+E2dXf0hjVkJphhGKnxAKZM8gzRL/cbAAAAAElFTkSuQmCC\" alt=\"p = 2\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.91667px; transform-origin: 19.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = 4\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a2 = 16\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAoCAYAAADJ/xXvAAADO0lEQVR4nO2aW7WrMBCGfw84wAAGUICCOsABDmoBDZUQD9tCNWCh5yH5F0PIlbJ329P51spLcynMLTPTAoqiKIqiKIryBO2L9n4dHYARwORGX7G3F/v8cQMwFJ7TALi4PaZy71fTwgrsERg/sMrNcY/sf7i5HA2A2a1fYBXZ1LzEN9PACo0KM9gr5I60Ii9unYmMnCf14hkMVHnV3GAF6Cuph1UqFXlLnHEHcD34/TSAB6wnKpW0sMKLeRnnGeJCHjJkzkjRifPVAw8yIe9BN6yCDimKd+kE61WlmWSDbdg+YgQKyoQ+IS7oHuFExrizS89NheqnkSk3022m0t9iORT2EpljQhIaN8RDpPTCAdaYLu7MESfIt8OapY2wipuxvejPLkBbxOusmlFT25XAcJoLu71b4yvVRNbKNTPCRlBa3uxgtnTH3opq6p5aYqGpdownPxeVUnPXXTPPNHnzkzi/8eZz5c2OlAIhDj6aTqc4yxPPDPOUx/TEXnqURHpeTJajWFN8ZzJVfiAcktrM/P8Gs8dnUn+G4gVbT5bdoZQsGQX8/UFk1yKmdVpWqF7qsE3FD8fyN2JGPCKVIh1DysNEPveRMs32T1NptP/F/kXdwr4skwp51qdyQaH1FxCS6xz53EfKMnvXy75dCJl0+PfDjH1I4EPWdN/fJTs9U4HAKjfp0VI5KRkVKzGlIJJy/5DQpsja0ud4VXZ6tgKZR/iJjWy3pZ63JELuFoasYsT2gi25Iwzqm7mvzk75S0JKgSzIS6FsQ4pisR+LfsB6J2bv5pQSL+4AHsYvnBH32hHW8j6pmdvBKjAV2hrY9+IaGt2I8LsyWYzJQpYQMcOjorMlTqiTzoKTFkBPnN0IZbADtmH3NxoCvwEVuCD+e6Bx8/Kd/HeVBtDCKu8Hac9mByxUxoyJuSAylZUFJjcv3ucpeK8cLZL/Eiqw9L6V7zME9vJH5cWtzQlf/prPprnM8K8FZ2wYsIYH33pqm9707lS8fwfYcC4dvkAb7wz2mWuvEtn8nrA2xF+OwT4rUz6MIxmq8kYwGdK/2n0IbBL7baUZn1VmfDWyD2hgMyr1QEVRFEVRFEVRFEX5Q/4BI4S3UXfFXN0AAAAASUVORK5CYII=\" alt=\"a3 = 256\" style=\"width: 56.5px; height: 20px;\" width=\"56.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1px 7.91667px; transform-origin: 17.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.492px 7.91667px; transform-origin: 125.492px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.475px 7.91667px; transform-origin: 103.475px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the corresponding values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2VUbWDMAyGPw84wAAGqgAFOKgDHMwCGpBQD1hAAxbYA8lpxsrY4ZTdh9vvnD4sWfPTpEmhUCgUCoU/ogE80ANObE5+N3eKBmAWcQcMwASssuo7hDsJPgPVzrca30+Frfgjt3BrgruEvz7xX6YCFgk8HvxHs7KQzspleuKpjm5xEH/IKQzx1EeBnfm4PqfwN4ED55m5hE15m/B7YmZurfdevGNru5HXsgzELPXin9hasBL/KraPNEY8yOZKgmq/68kHWfuO0LK04nfEaXg6CfVkdo3EFC87+55FPjQQZ8As66sx3LKd1ic2fHpMbOa82HQgHc2MbOidmYiZ0oHkjzblQuvdGZteuNueXSX1EM3GlmrfLOiAsrXVOzCwtd5t4g/e50PNdvsXXktRKBT+CU+MO3Oqf1KjkgAAAABJRU5ErkJggg==\" alt=\"a_n\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5833px 7.91667px; transform-origin: 85.5833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand returns the initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,a0] = recurrence1(n,a)\r\n  p = f1(n,a);\r\n  a0 = f2(n,a);\r\nend","test_suite":"%%\r\na = [16 65536];\r\nn = [2 4];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [512 134217728];\r\nn = [2 3];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [0.840896415253715 0.999994711720674];\r\nn = [2 17];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/2;\r\na0_correct = 1/2;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-10)\r\n\r\n%%\r\na = [3.236570233533632 6.5197372744901154];\r\nn = [53 100];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1.01;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [27.065907669081142 6576132142.795870];\r\nn = [4 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = (1+sqrt(5))/2;\r\na0_correct = (1+sqrt(5))/2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [1.033024879021228 1.000000123944382];\r\nn = [2 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/8;\r\na0_correct = 8;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-9)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-02T16:23:14.000Z","updated_at":"2026-01-13T13:35:21.000Z","published_at":"2021-04-02T16:27:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the difference equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_{n+1} = a_n^p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_{n+1} = a_n^p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the initial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a2 = 16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2 = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a3 = 256\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_3= 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the corresponding values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand returns the initial value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":51274,"title":"Solve a nonlinear difference equation","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 95.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.875px; transform-origin: 407px 47.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.25px; text-align: left; transform-origin: 384px 22.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.967px 7.91667px; transform-origin: 102.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the difference equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_{n+1} = a_n^p\" style=\"width: 60.5px; height: 22px;\" width=\"60.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 7.91667px; transform-origin: 48.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the initial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.91667px; transform-origin: 22.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 7.91667px; transform-origin: 28.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 2\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.91667px; transform-origin: 19.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = 4\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a2 = 16\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a3 = 256\" style=\"width: 56.5px; height: 20px;\" width=\"56.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1px 7.91667px; transform-origin: 17.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.492px 7.91667px; transform-origin: 125.492px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.475px 7.91667px; transform-origin: 103.475px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the corresponding values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2VUbWDMAyGPw84wAAGqgAFOKgDHMwCGpBQD1hAAxbYA8lpxsrY4ZTdh9vvnD4sWfPTpEmhUCgUCoU/ogE80ANObE5+N3eKBmAWcQcMwASssuo7hDsJPgPVzrca30+Frfgjt3BrgruEvz7xX6YCFgk8HvxHs7KQzspleuKpjm5xEH/IKQzx1EeBnfm4PqfwN4ED55m5hE15m/B7YmZurfdevGNru5HXsgzELPXin9hasBL/KraPNEY8yOZKgmq/68kHWfuO0LK04nfEaXg6CfVkdo3EFC87+55FPjQQZ8As66sx3LKd1ic2fHpMbOa82HQgHc2MbOidmYiZ0oHkjzblQuvdGZteuNueXSX1EM3GlmrfLOiAsrXVOzCwtd5t4g/e50PNdvsXXktRKBT+CU+MO3Oqf1KjkgAAAABJRU5ErkJggg==\" alt=\"a_n\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5833px 7.91667px; transform-origin: 85.5833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand returns the initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,a0] = recurrence1(n,a)\r\n  p = f1(n,a);\r\n  a0 = f2(n,a);\r\nend","test_suite":"%%\r\na = [16 65536];\r\nn = [2 4];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [512 134217728];\r\nn = [2 3];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [0.840896415253715 0.999994711720674];\r\nn = [2 17];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/2;\r\na0_correct = 1/2;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-10)\r\n\r\n%%\r\na = [3.236570233533632 6.5197372744901154];\r\nn = [53 100];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1.01;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [27.065907669081142 6576132142.795870];\r\nn = [4 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = (1+sqrt(5))/2;\r\na0_correct = (1+sqrt(5))/2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [1.033024879021228 1.000000123944382];\r\nn = [2 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/8;\r\na0_correct = 8;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-9)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-02T16:23:14.000Z","updated_at":"2026-01-13T13:35:21.000Z","published_at":"2021-04-02T16:27:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the difference equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_{n+1} = a_n^p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_{n+1} = a_n^p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the initial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a2 = 16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2 = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a3 = 256\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_3= 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the corresponding values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand returns the initial value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"difference equation\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"difference equation\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"difference equation\"","","\"","difference equation","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f3034928540\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f30349284a0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f3034927be0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f30349287c0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f3034928720\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f3034928680\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f30349285e0\u003e":"tag:\"difference equation\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f30349285e0\u003e":"tag:\"difference equation\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday 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equation\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"difference equation\"","","\"","difference equation","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f3034928540\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f30349284a0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f3034927be0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f30349287c0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f3034928720\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f3034928680\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f30349285e0\u003e":"tag:\"difference equation\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f30349285e0\u003e":"tag:\"difference equation\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":51274,"difficulty_rating":"easy-medium"}]}}