An unbounded sequence and a divergent sequence where the difference is convergent

Question

Any kind of narration helps with understanding. please note that there must be two different sequences.

Or state that it is impossible.

Answer 1

Let a_{n}=n+(1/n) and b_{n}=n. Both of these sequences are unbounded and diverge to infinity. But the sequence a_{n}-b_{n}=1/n converges to 0.