# What is the tenth term of the geometric sequence with a4 = 16 and r = 2?

Feb 23, 2016

1024

#### Explanation:

for the standard 'Geometric sequence' , the terms are

a , ar , $a {r}^{2} , a {r}^{3} , a {r}^{4} , \ldots \ldots \ldots \ldots \ldots \ldots . . , a {r}^{n - 1}$

where a , is the 1st term , r is the common ratio and the
nth term = $a {r}^{n - 1}$
To find any term in the sequence , the nth term is used. To use it , requires knowing a and r .

To find a.

use ${a}_{4} = a {r}^{3} = 16 \Rightarrow a = \frac{16}{r} ^ 3 = \frac{16}{2} ^ 3 = \frac{16}{8} = 2$

now ${a}_{10} = a {r}^{9} = 2 {\left(2\right)}^{9} = 1024$