Question

What is the sum of the geometric sequence 1, 4, 16, … if there are 8 terms?

Answer 1

The the sum of the geometric sequence 1, 4, 16, … up to 8 terms is 21845.

Explanation:

Given the geometric series 1, 4, 16, …

we have to find the sum of the GP if there are 8 terms.

Series: 1, 4, 16, …

First term, a=1

Number of terms, n=8

Common ratio,
`r=(4)/(1)=(16)/(4)=4`

The formula to find the sum of above G.P is

`S_n=(a(r^n-1))/(r-1)`

`=(1(4^8-1))/(4-1)=(65536-1)/(3)=(65535)/(3)=21845`

Hence, the the sum of the geometric sequence 1, 4, 16, … up to 8 terms is 21845.

Answer 2

The sum of geometric sequence:
S n = a 1 * ( q^n - 1 ) / ( q - 1 )
where: a 1 = 1,
q = a 2 : a 1 = 4 : 1 = 4
S 8 = 1 * ( 4^(8) - 1 ) / ( 4 - 1 ) =
= ( 65,536 - 1 ) / ( 4 - 1 ) = 65,535 / 3 = 21,845