Question

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

−959,781
29,637
26,661
959,780

Answer 1

The sum of 8 geometric sequence is 959780

Explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so,
`a_1=-4`

now, we can find common ratio

`r=(24)/(-4)=-6`

we can use formula

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

n=8

now, we can plug values

`S_8=-4((1-(-6)^(8))/(1+6) )`

now, we can simplify it

and we get

`S_8=959780`