Question

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

Answer 1

You can tell if `f(n+1)/f(n)=`some number that is the same for all the numbers in the series

Explanation:

`10/5=2`

`20/10=2`

`40/20=2`

`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.