Question

How do you find the sum of the first 14 terms of `1+4+16+64+...`?

Answer 1

Sum if first `14` terms is `89478485`

Explanation:

This is a geometric series. In geometric series, if `a_1` is first term and `r` is constant ratio of any term to its preceding term, then `n^(th)` term of the sequence is given by `a_n=a_1×r^(n-1)` and sum of the series up to `n^(th)` term is given by `a_1(r^n-1)/(r-1)`.

In the given series first term `a_1=1` and ratio `r=4/1=16/4=64/16=4`. Hence sum of the series up to `14^(th)` term is

`1×(4^14-1)/(4-1)=(268435456-1)/3=89478485`