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

1 Answer
Sep 2, 2016

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