Explanation:

Cauchy Sequence:
A Cauchy sequence is a sequence of numbers in which the terms become arbitrarily close to each other as the sequence progresses. Formally, a sequence {an} is called a Cauchy sequence if for every positive real number ε, there exists a positive integer N such that |an - am| < ε="" for="" all="" n,="" m="" /> N.

Not a Cauchy Sequence:
If a sequence is not a Cauchy sequence, it means that there exists a positive real number ε for which it is not possible to find a positive integer N such that |an - am| < ε="" for="" all="" n,="" m="" /> N. In other words, there exists a pair of terms in the sequence that do not get arbitrarily close to each other as the sequence progresses.

Divergent Sequence:
A divergent sequence is a sequence that does not have a finite limit. It means that the terms of the sequence do not approach a specific value as the sequence progresses.

Convergent Sequence:
A convergent sequence is a sequence that has a finite limit. It means that as the sequence progresses, the terms of the sequence approach a specific value.

Bounded Sequence:
A bounded sequence is a sequence in which the terms are limited to a specific range. It means that there exist positive real numbers M and L such that |an| ≤ M for all n and |an - am| ≤ L for all n, m.

Conclusion:
If a sequence is not a Cauchy sequence, it means that there exists a pair of terms in the sequence that do not get arbitrarily close to each other as the sequence progresses. This implies that the terms of the sequence do not approach a specific value, and therefore the sequence does not have a finite limit. Hence, the sequence is divergent (option A). It does not necessarily mean that the sequence is bounded, as there could be terms in the sequence that become arbitrarily large.