# How do you find the indicated term of the geometric sequence where a_1=4096, r=1/4, n=8?

Feb 21, 2017

${a}_{8} = \frac{1}{4.}$

#### Explanation:

The General ${n}^{t h}$ Term ${a}_{n}$ of a Geom. Seq. is given by,

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

In our Example, ${a}_{1} = 4096 , r = \frac{1}{4} , n = 8.$

$\therefore {a}_{8} = \left(4096\right) {\left(\frac{1}{4}\right)}^{8 - 1} = \frac{4096}{4} ^ 7 = {4}^{6} / {4}^{7.}$

$\therefore {a}_{8} = \frac{1}{4.}$