Question

What is the next term in the sequence `1/3, 2/9, 3/27`?

Answer 1

`0` or `4/81` or anything you like.

Explanation:

This sequence, equal to `3/9, 2/9, 1/9` has a common difference `-1/9`, so is an arithmetic sequence. If it continues as an arithmetic sequence, then the next term is `0`.

However, note that the way the question is posed with the given choice of numerators and denominators. It appears that the numerators are following an arithmetic sequence `(1, 2, 3)` and the denominators a geometric sequence `(3, 9, 27)`.

If that is the intent, then the next number in the sequence would be `4/81`.

In fact, the next number could be anything, since we have not been told what kind of sequence this is.