Question

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

Answer 1

`\large\boxed{21845}`

Explanation:

The formula of a sum of terms of a geometric sequence:

`S_n=a_1\cdot(1-r^n)/(1-r)`

We have:

`a_1=1,\ a_2=4,\ a_3=16\ and\ n=8`

Calculate the common ratio:

`r=(a_2)/(a_1)=(a_3)/(a_2)=...=(a_(n+1))/(a_n)\\\\r=(4)/(1)=4\\\\r=(16)/(4)=4`

CORRECT :)

Substitue:

`S_8=1\cdot(1-4^8)/(1-4)=(1-65536)/(-3)=(-65535)/(-3)=21845`