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?
This is not a geometric sequence, since there is no common ratio.
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:
These three ratios are not equal. In fact, the ratios are getting smaller (approaching unity).