Question

How do you determine whether the sequence `1/5, 2/7, 3/9, 4/11,...` is geometric and if it is, what is the common ratio?

Answer 1

This is not a geometric sequence, since there is no common ratio.

Explanation:

If it was a geometric sequence, it would show a common ratio, but this sequence does not. All you need do is test a few consecutive terms to see this:

`3/9 -: 2/7 = 3/9 xx 7/2 = 21/18 = 7/6`

`4/11 -: 3/9 = 4/11 xx 9/3 = 36/33 = 12/11`

`5/13 -: 4/11 = 5/13 xx 11/4 = 55/52`

These three ratios are not equal. In fact, the ratios are getting smaller (approaching unity).