# How do you tell whether the sequence 5, 10, 20, 40, 80, ... is geometric?

Mar 15, 2017

You can tell if $f \frac{n + 1}{f} \left(n\right) =$some number that is the same for all the numbers in the series

#### Explanation:

$\frac{10}{5} = 2$

$\frac{20}{10} = 2$

$\frac{40}{20} = 2$

$\frac{80}{40} = 2$

All these terms have a common ratio of 2. That means, if you take the next term up and divide it with the first term, you will always get this common ratio if it's a geometric series.
Since when you divide them, you always get the common ratio, that means the series is geometric.