Report r_n and n when |r_n − r_n−1|< 10−9 (while-loop).

I was asked to create a while loop for Fibonacci sequence

with initial values: Fn= Fn−1 + Fn−2,

F0 = 2 and F1 = 3

note r_n= Fn+1/Fn

It wants me to report r_n and n when |rn−rn−1|< 10−9 (while-loop)

Code created:

fib_first = 2;
fib_second = 3;
fib_all = zeros(n, 1); 
fib_all(2) = fib_first;
fib_all(3) = fib_second;
n=1:100
fib_all(ii) = fib_all(ii-1)+fib_all(ii-2)
while abs(r_n - r_n-1) < 10^-9
end

I am having a hard time understanding what I am doing wrong. I do not feel confident with this code.

[Dyuman Joshi]

Is r(n)

%1
F(n+1)/F(n)

%2
(F(n)+1)/F(n)

%3
F(n)+(1/F(n))

[LILIA VERGARA]

Hi- r(n) is %1

Answer 1

[Dyuman Joshi]

You have to update the values inside the while loop. One way to do is

F=[2 3 5];
%defining rn = F(n+1)/F(n)
r=F(2:3)./F(1:2);
n=2;
while abs(diff(r))>=1e-9
    F=[F(2:3) F(2)+F(3)];
    r=F(2:3)./F(1:2);
    n=n+1;
end
F

F = 1×3

28657 46368 75025

n

n = 22

rn=r(end)

rn = 1.6180