Question

Find the sum of the geometric series: $-2+6-18+54-162$.

• A. $-111$
• B. $-122$
• C. $-133$
• D. $-144$

Answer 1

Answer: (B)

$-122$

Given series is $-2+6-18+54-162$

First term, $a$ is $-2$
Common ratio, $r=$ $\frac{6}{-2}=-3$
Use the formula for the sum of the geometric series.
$S=a\left[\frac{r^n-1}{r-1}\right]$

$S=-2\left[\frac{(-3{)}^5-1}{(-3)-1}\right]$

$S=-2\times \frac{244}{4}$

$S=-2\times 61$
$S=-122$