# How do you write an nth term rule for 5,-5/3,5/9,-5/27,... and find a_6?

Apr 28, 2018

See below

#### Explanation:

Geometric sequence explicit formula:
${a}_{n} = {a}_{1} {\left(r\right)}^{n - 1}$

Determine $r$ which is the decay factor:
$r = - \frac{5}{3} \cdot \frac{1}{5} = - \frac{1}{3}$

Substitute into the equation for the rule:
${a}_{n} = 5 {\left(- \frac{1}{3}\right)}^{n - 1}$

For the sixth term:
${a}_{6} = 5 {\left(- \frac{1}{3}\right)}^{6 - 1} = - \frac{5}{243}$