Question

The first term of a geometric series is -1, and the common ratio is -3. how many terms are in the series if its sum is 182?

Answer 1

There are `6` terms.

Explanation:

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

`182 = (-1(1 - (-3)^n))/(1 - (-3))`

`182(4) = -1(1 - (-3)^n)`

`-728= 1 - (-3)^n`

`-729 = -(-3)^n`

`729= (-3)^n`

`-3^6 =-3^n`

`n = 6`

Hopefully this helps!