I'm not sure I believe that the equation given in your attached image is correct. However, the changes below allow the code to run so that you can work out the details.
%initial conditions
g0 = 9.81; %m/s^2
R = 6.37e6; %m
h = 10000; %Step Size in m
x = 0 : h : 100000; % Range of X values
v = zeros(size(x));
v(1) = 1400; %m/s Initial velocity <<<<< initialize the first element of v
n = numel(v); % Number of values for velocity
for i=1:(n-1)
v(i+1) = v(i) + ((g0/v(i)) * (R^2/ ((R + x(i))^2))) * (x(i+1) - x(i));
% ^^-----^^----------^^------index using i rather than x(i)
end
plot (x,v) % << change to plot the entire v vector against the entire x vector
grid on
