Fibonacci sequence

The Fibonacci sequence starts with $1, 1$, and each next term is the sum of the two preceding ones:

$F_1=1,\ F_2=1,\qquad F_n=F_{n-1}+F_{n-2}$

giving $1, 1, 2, 3, 5, 8, 13, 21, 34, 55\dots$ What is fascinating is that the ratio of consecutive terms $\dfrac{F_n}{F_{n-1}}$ approaches the golden ratio:

$\varphi=\frac{1+\sqrt5}{2}\approx1.618$

The sequence and the golden ratio appear in nature — in the arrangement of sunflower seeds, in seashells and in plant branching. Enter the term index (up to 90).