Question

NEED HELP ASAP!!! What is the sum of the geometric sequence -4, 24, -144, ... if there are 8 terms?

A. -959,781

B. 29,637

C. 26,661

D. 959,780

Answer 1

D

Explanation:

the sum to n terms of a geometric sequence is

`S_(n)` =
`(a_(1)(r^(n)-1) )/(r-1)`

where a₁ is the first term and r the common ratio

here a₁ = - 4 and r =
`(a_(2) )/(a_(1) )` =
`(24)/(-4)` = - 6 , then

S₈ =
`(-4((-6)^(8)-1) )/(-6-1)`

=
`(-4(1679616-1))/(-6-1)`

=
`(-4(1679615))/(-7)`

=
`(-6718460)/(-7)`

= 959,780