Question

How to find the indicated term of the Fibonacci Sequence? 13th term

Answer 1

Fibonacci squence is constructed by following recurrence formula

`a_(n-1)+a_n=a_(n+1)` or equivalents. It say, each term is the sum of two prior terms starting by `1,1`. Lets see

`1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ....`

So the 13th term is 233.

It's hard to find out a general term for Fibonacci squence. You can see a general term expresed by

`a_n=1/sqrt5[((1+sqrt5)/2)^n-((1-sqrt5)/2)^n]`