Question

What is the sum of the first six terms of the geometric series?

2 – 6 + 18 – 54 +

Answer 1

S₆ = - 364

Explanation:

the sum to n terms of a geometric series is

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

where a₁ is the first term and r the common ratio

here a₁ = 2 and r =
`(a_(2) )/(a_(1) )` =
`(-6)/(2)` = - 3 , then

S₆ =
`(2((-3)^(6)-1) )/(-3-1)`

=
`(2(729-1))/(-4)`

=
`(2(728))/(-4)`

=
`(1456)/(-4)`

= - 364