Explanation:
An increasing sequence is a sequence of numbers where each term is greater than or equal to the previous term. In other words, if we have a sequence (a1, a2, a3, ...) such that ai ≤ ai+1 for all i, then the sequence is increasing.

Convergence:
Convergence refers to the behavior of a sequence as the number of terms increases. If a sequence converges, it means that its terms get closer and closer to a certain value as we take more terms. In this case, the supremum of the sequence is the maximum limit or the largest value that the sequence approaches.

Supremum:
The supremum of a set is the least upper bound or the smallest value that is greater than or equal to all the elements of the set. In the context of a sequence, the supremum is the maximum limit or the largest value that the sequence approaches.

Explanation of the answer:
If a sequence is increasing, it means that each term is greater than or equal to the previous term. In this case, as the terms of the sequence become larger, they cannot exceed the supremum of the sequence because the supremum is the smallest value that is greater than or equal to all the elements of the sequence.

Therefore, if the sequence is increasing, it will converge to its supremum because the terms of the sequence can only get closer and closer to the supremum without exceeding it. This is why option A, "converges to its supremum," is the correct answer.

Other options:
- Option B, "diverges," is incorrect because an increasing sequence does not diverge. Divergence occurs when the terms of a sequence do not approach a specific value or limit.
- Option C, "may converge to its supremum," is incorrect because an increasing sequence will always converge to its supremum.
- Option D, "is bounded," is incorrect because an increasing sequence can be unbounded, meaning it does not have an upper limit. However, if the sequence is bounded, it will still converge to its supremum.