How do I check whether a given sequence is actually an arithmetic progression?

A sequence is an arithmetic progression only if the difference between consecutive terms is constant. So to check, compute the difference between several consecutive pairs: second minus first, third minus second, fourth minus third, and so on. If all these differences are equal, the sequence is an AP and that common value is the common difference d. For example, in 7, 10, 13, 16, the differences are 3, 3, 3, all equal, so it is an AP with d = 3. In 1, 4, 9, 16, the differences are 3, 5, 7, which are not equal, so it is not an AP. In an exam, showing that aₙ₊₁ − aₙ is the same for all consecutive terms is enough to prove it.