Question

What is the sum of the geometric sequence −1, 6, −36, … if there are 6 terms?

Answer 1

First term, a = -1
Common ratio, r = 6/-1 = -6
Sum of n terms of GP is
$\frac{a( {r}^{n} - 1) }{r - 1} \: \: \: for \: \: |r| > 1 \\ = \frac{ - 1 \times ( { (- 6)}^{6} - 1) }{ - 6 - 1} = \frac{ {6}^{6} - 1}{7} \\ = 6665$