% Example Program for Fibonacci Sequence
% Author: F. P. Schloerb

% clear the workspace initially to allow rerunning with different
% numbers of elements in the sequence
clear

% initialize the first two terms in the sequence
% note that MATLAB indexing is one-off traditional indexing
% for Fibonacci Sequence
f(1) = 0;
f(2) = 1;

% initialize golden ratio "sequence" with zeros
r(1) = 0.0; % r is undefined so set to zero
r(2) = 0.0; % r is infinite (1/0) so set to zero

% ask the user for number of terms to compute
n = input('Enter number of terms of series to compute');

% now do the sequence through index of n (input above)
for i=3:n
    f(i) = f(i-1)+f(i-2);
    r(i) = f(i)/f(i-1);
end

% print resulting arrays
f
r

% plot successive approximations to golden ratio
plot(1:n,r);