# How do you write a rule for the nth term of the geometric sequence and then find a_5 given a_3=-144, r=0.5?

Dec 15, 2017

${a}_{n} = - 576 {\left(0.5\right)}^{n - 1} , {a}_{5} = - 36$

#### Explanation:

$\text{the nth term of a geometric sequence is }$

•color(white)(x)a_n=ar^(n-1)

$\text{where a is the first term and r the common ratio}$

${a}_{3} = a {r}^{2} = - 144$

$\Rightarrow a = - \frac{144}{0.25} = - 576 \leftarrow \textcolor{b l u e}{\text{first term}}$

$\Rightarrow {a}_{n} = - 576 {\left(0.5\right)}^{n - 1}$

$\Rightarrow {a}_{5} = - 576 \times {\left(0.5\right)}^{4} = - 36$