What is the difference between an AP and a GP and how do I tell them apart?

In an arithmetic progression (AP) you get the next term by adding a fixed number called the common difference d, so consecutive terms differ by the same amount. In a geometric progression (GP) you get the next term by multiplying by a fixed number called the common ratio r, so consecutive terms have the same ratio. To test a sequence, subtract consecutive terms: if the differences are constant it is an AP. Then divide consecutive terms: if the ratios are constant it is a GP. For example 2, 5, 8, 11 is an AP with d = 3. And 3, 6, 12, 24 is a GP with r = 2. The nth term of an AP is a + (n−1)d, and of a GP is a·r^(n−1).