# How do you write an equation for the nth term of the geometric sequence 64,16,4,....?

Jan 2, 2017

$64 {\left(\frac{1}{4}\right)}^{n - 1}$

#### Explanation:

This is a geometric sequence with starter

a = 64 and common ratio

r = 16/64=4/16=1/4 ..

The generall $\left({n}^{t h}\right)$ term is

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

$= 64 {\left(14\right)}^{n - 1}$

For exemplification,

the ${4}^{t h}$ term is $64 {\left(\frac{1}{4}\right)}^{3} = \frac{64}{64} = 1$ and

the ${10}^{t h}$ term is $64 {\left(\frac{1}{4}\right)}^{9} = \frac{64}{262144} = \frac{1}{4096}$.