# How do you find a_9 for the geometric sequence 1/5, 1, 5,...?

Oct 23, 2016

.${a}_{9} = {5}^{7} = 78125$

#### Explanation:

The GP $\frac{1}{5} , 1 , 5. \ldots$

comparing with the standard GP $a , a r , a {r}^{2} , \ldots .$

we note the first term

$= \frac{1}{5}$

and the common ratio is $r = 5$

$\therefore {a}_{n} = a {r}^{n} - 1$

so ${a}_{9} = \left(\frac{1}{5}\right) {5}^{8}$

ie..${a}_{9} = {5}^{7} = 78125$