Question

What is the sum of the geometric sequence -3,18,-108,.. if there are 7 terms?

Answer 1

`S_(7)` = - 119973

Explanation:

The sum to n terms of a geometric sequence is

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

where a is the first term and r the common ratio

Here a = - 3 and r = 18 ÷ - 3 = - 6 , thus

`S_(7)` =
`(-3(-279936-1))/(-6-1)`

=
`(-3(-279937))/(-7)`

=
`(839811)/(-7)`

= - 119973