Question

Determine whether the sequence is arithmetic, geometric, both, or neither. 1, 4, 9, 16, 25, . . .

Answer 1

neither

Explanation:

First differences are 3, 5, 7, 9, and the differences of these (2nd differences) are constant at 2. The degree of the polynomial function describing the sequence is equal to the number of the differences that are constant. Here, that is 2nd differences, so the sequences is described by a 2nd-degree (quadratic) polynomial.

It is not linear (arithmetic) or exponential (first differences have a common ratio).