Question

How do you find the number of terms given `s_n=341` and `1+4+16+64+...`?

Answer 1

`n=5`

Explanation:

This is a geometric series with first term `a_1=1` and common ratio `r` as

`4/1=16/4=64/16=4`

The sum of such a series for first `n` terms is given by

`S_n=a_1xx(r^n-1)/(r-1)` and as `S_n=341`, `a_1=1` and `r=4` and , we have

`1xx(4^n-1)/(4-1)=341`

or `(4^n-1)/3=341`

or `4^n-1=341xx3=1023`

and `4^n=1023+1=1024=4^5`

Hence, `n=5`