# How do you write a rule for the nth term of the geometric sequence and then find a_5 given a_1=17, r=-2?

Mar 15, 2017

${a}_{5} = 272.$

#### Explanation:

In the Usual Notation for Geo. Seq.,

${a}_{n} = {a}_{1} \cdot {r}^{n - 1} , n \in \mathbb{N} .$

With, ${a}_{1} = 17 , \mathmr{and} , r = - 2 ,$ we have,

${a}_{n} = 17 {\left(- 2\right)}^{n - 1} , n \in \mathbb{N} .$

Accordingly, ${a}_{5} = 17 {\left(- 2\right)}^{5 - 1} = \left(17\right) \left(16\right) = 272.$