Question

Find the sum of the following geometric sequences a) 6 terms (-4, 12, -36,...)​

Answer 1

S₆ = 728

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) )` =
`(12)/(-4)` = - 3 , then

S₆ =
`(-4((-3)^(6)-1) )/(-3-1)`

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

= 729 - 1

= 728