# How do you determine whether the sequence 1/8, 1/4, 1/2, 1,... is geometric and if it is, what is the common ratio?

Mar 2, 2017

$r = 2$

#### Explanation:

A sequence is geometric if it has the same common ratio between each term.

The common ratio is the number you multiply it by to get the next one, so,

$\frac{1}{8} \times r = \frac{1}{4}$

$\frac{1}{4} \times r = \frac{1}{2}$

etc.

You can rearrange these to say that

$r = \frac{\frac{1}{4}}{\frac{1}{8}} = 2$

$r = \frac{\frac{1}{2}}{\frac{1}{4}} = 2$

You can see from these (and if you want to work out the others) that the common ratio is always the same, so the series is geometric.

You can also see that $r = 2$.