Say the first two terms of a sequence are $a_0,a_1$, then the remaining terms meet the formula $$a_{n+2}=a_{n+1}+a_n$$
What is the $n_{th}$ term formula?
I figured that $$\lim_{n \rightarrow \infty}\frac{a_{n+1}}{a_n}=\Phi = \frac{1+\sqrt 5}{2}\approx 1.618$$
Using this fact, find the $n_{th}$ term formula for the Fibonacci Series.
Best Answer
A proof can be found here involving matrices and eigenvectors.