# What is the sum of the geometric sequence -4,24,-144,... if there are 8 terms?

May 17, 2018

$959780$

#### Explanation:

Sum of geometric sequence is $\frac{a \left({r}^{n} - 1\right)}{r - 1}$
where
r = the ratio
n = number of terms

In this case,

a = -4
r = $\frac{24}{-} 4 = - \frac{144}{24} = - 6$
n = 8

Sum
= $\frac{a \left({r}^{n} - 1\right)}{r - 1}$

= $\frac{- 4 \left({\left(- 6\right)}^{8} - 1\right)}{- 6 - 1}$

= $\frac{- 4 \times 1679615}{-} 7$

= $- \frac{6718460}{-} 7$

= $959780$