# How do you write the expression for the nth term of the geometric sequence a_1=64, r=-1/4, n=10?

Jul 25, 2017

$\frac{256}{5} \left(1 - {\left(- \frac{1}{4}\right)}^{n}\right)$

#### Explanation:

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

•color(white)(x)a_n=(a(1-r^n))/(1-r)larra=a_1

$\Rightarrow {a}_{n} = \frac{64 \left(1 - {\left(- \frac{1}{4}\right)}^{n}\right)}{1 + \frac{1}{4}}$

$\textcolor{w h i t e}{\Rightarrow {a}_{n}} = \frac{256}{5} \left(1 - {\left(- \frac{1}{4}\right)}^{n}\right)$