Question

How do you find the sum of the first 5 terms of the geometric series: 4+ 16 + 64…?

Answer 1

`1364`

Explanation:

`a_2/a_1=16/4=4`
`a_3/a_2=64/16=4`

`implies` common ratio`=r=4` and `a_1=4`

Sum of a geometric series is given by
`Sum=S=(a(1-r^n))/(1-r)`

Where `a` is the first term `r` is the common ratio and `n` is the number of terms.

#Sum=S=(4(1-4^5))/(1-4)=(4(1-1024))/(-3)=(4(-1023))/(-3)=(-4092)/(-3)=1364#

Hence the required sum is `1364`.