# What is the 9th term of the geometric sequence where a1 = -7 and a6 = -7,168?

Jan 9, 2016

${a}_{9} = - 7 \cdot {4}^{8} = - 458752$

#### Explanation:

The general term of a geometric sequence can be written:

${a}_{n} = a {r}^{n - 1}$

where $a$ is the initial term and $r$ is the common ratio.

We are given:

$a = {a}_{1} = - 7$

$a {r}^{5} = {a}_{6} = - 7168$

So $r = \sqrt[5]{\frac{- 7168}{-} 7} = \sqrt[5]{1024} = \sqrt[5]{{4}^{5}} = 4$

(assuming we are dealing with a Real geometric sequence)

Then ${a}_{9} = a {r}^{8} = - 7 \cdot {4}^{8} = - 7 \cdot 65536 = - 458752$