Question

what is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4? −32,766 −19,662 19,662 32,766

Answer 1

sum of ggeo metric sequence is

Sn=
`(a1(1-r^n))/(1-r)`

n=which term
a1=first term
r=common ratio


so
n=7
a1=-6
r=-4

Sn=
`(-6(1-(-4)^7))/(1-(-4))`
Sn=
`(-6(1-(-16384)))/(1+4)`
Sn=
`(-6(1+16384))/(5)`
Sn=
`(-6(16385))/(5)`
Sn=
`(-98310)/(5)`
Sn=-19662

answer is 2nd option os -19662