Question

Find the sum of the geometric series given a1=2, r=−3, and n=8.

Answer 1

S₈ = - 3280

Explanation:

The sum to n terms of a geometric series is

`S_(n)` =
`\frac{a_{}(r^(n)-1) }{r-1}`

Here a₁ = 2, r = - 3 and n = 8 , then

S₈ =
`(2((-3)^(8)-1) )/(-3-1)`

=
`(2(6561-1))/(-4)`

=
`(2(6560))/(-4)`

=
`(13120)/(-4)`

= - 3280