Answer
See explanation
Work Step by Step
Sequence could diverge in one of the ways:
1) Sequence goes unbounded for increasing values of index. E.g., $n,{n^2},{e^n}$ etc.
2) Sequence remains bounded but keeps on oscillating. E.g., different sequence for even and odd terms which converge to different values, ${\sin(n)}$ etc.
3) Sequence (bounded or not) does not have limit
