# How do you find the sum of the infinite geometric series -3, -3/2, -3/4, -3/8?

Nov 21, 2015

The sum of this sequence is $- 6$

#### Explanation:

To find the sum of an infinite geometric sequence we use the formula:

$S = {a}_{1} / \left(1 - q\right)$

First we have to find $q$ to see if the sequence is convergent:

$q = - \frac{3}{2} : \left(- 3\right) = \frac{1}{2}$

$\left\mid q \right\mid < 1$, so the sequence is convergent. We can calculate the sum:

$S = {a}_{1} / \left(1 - q\right) = \frac{- 3}{1 - \frac{1}{2}} = - \frac{3}{\frac{1}{2}} = - 3 \cdot 2 = - 6$