# What is the 7th term of the geometric sequence where a1 = –2 and a5 = –512?

Feb 23, 2016

$8192$

#### Explanation:

First recognise that $- 512$ is a power of $- 2$; specifically $- 512 = {\left(- 2\right)}^{9}$

As this is the fifth term, the power is $2 \cdot 5 - 1 = 9$

The $n$th term is therefore ${\left(- 2\right)}^{2 n - 1}$

The $7$th term will be ${\left(- 2\right)}^{2 \cdot 7 - 1} = {\left(- 2\right)}^{13} = 8192$