# What is the sum of the first 6 terms of this geometric sequence –4, –16, –64, –256?

The sum is $- 5460$

#### Explanation:

The sum of a geometric progession is given by

$S = a \cdot \frac{1 - {r}^{n}}{1 - r}$ where a is the first of the progression and r is the ratio of the progession. To find it we divide two terms of the progession hence we have that

$r = - \frac{16}{-} 4 = 4$

So the sum is

$S = \left(- 4\right) \cdot \frac{{\left(4\right)}^{6} - 1}{4 - 1} = - 5460$