Consider the sequence: 7, 13, 19, 25, 31,… Which expression describes this sequence, using n to represent the position of a term in the sequence, where n=1 for the first term?

Answer 1

First take the differences: 13–7 = 19–13 = 25–19 = 31–25 = 6. So, we know there is a 6n in the expression. Then subtract 6n from each term: 7–6 = 13–12 = 19–18 = 25–24 = 31–30 = 1. Therefore, the full expression is 6n+1.

Answer 2