# Given the geometric series 1/6 + 1/36 + 1/216+ ..., what is the common ratio r?

Jun 7, 2017

$\frac{1}{6}$

#### Explanation:

$r$ is the common ratio in the geometric series--in other words, it is what you multiply the $n$th term to get the $n + 1$ term.

So,

$\frac{1}{6} r = \frac{1}{36}$

$r = \frac{1}{6}$

Jun 7, 2017

$r = \frac{1}{6}$

#### Explanation:

To find the common ratio of any geometric series, we must find the quotient of any two consecutive terms:

$R i g h t a r r o w r = \frac{1}{36} \div \frac{1}{6}$

$R i g h t a r r o w r = \frac{1}{36} \times \frac{6}{1}$

$\therefore r = \frac{1}{6}$

Therefore, the common ratio $r$ of the geometric series is $\frac{1}{6}$.