Question

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

Answer 1

`8192`

Explanation:

First recognise that `-512` is a power of `-2`; specifically `-512 = (-2)^9`

As this is the fifth term, the power is `2*5-1 = 9`

The `n`th term is therefore `(-2)^(2n-1)`

The `7`th term will be `(-2)^(2*7-1) = (-2)^13 = 8192`