How Many Interations Does It Take Before Successive Iterations Do Not Change More Than 1E-6?

This is Fibonacci's sequence and f3 is each element in the sequence divided by the one before it. This is supposed to demonstrate the Golden Ratio. However, I need my code to tell me how many times elements there are before each successive element is no greater than 10^-6 before it. I'm pretty sure I need to use a while loop, but I still can't get it right....

%fib seq using Binet Eq
  a= 1:10;
    b= sqrt(5);
    x = (1-b)/2;
    y = (1+b)/2;
    f = (y.^a - x.^a)./b;
    fb=reshape(f,[],5)

    %ratio
      c=a+1;
      f2 = (y.^c - x.^c)./b;
      f3=f2./f;

Answer 1

[Santhana Raj]

The equation of b, x and y can be outside the loop and same as your definitions.

 k=1;
  while true
      k=k+1;
      f(k) = (y.^k - x.^k)./b;
      c=k+1;
      f2(k) = (y.^c - x.^c)./b;
      f3(k)=f2(k)/f(k);

      if(abs(f3(k)-f3(k-1))<10e-6)
          break;
      end
  end

Hope it helps.