Question

Determine whether the following sequence is arithmetic, geometric, or neither.

1, 4, 9, 16, ...


A.arithmetic
B.geometric
C.neither

Answer 1

neither. if it was arithmetic there would be a common difference

if it we geometric there would be a common ratio

there is neither so it is neither

Answer 2

Well, for arithmetic sequences, there is a common difference between each term. In this one, the differences are 3, 5, 7, 9, etc. The difference is not the same, so it is not a arithmetic sequence.

For geometric sequences, there is a common ratio between each term. In this, the ratios are 4, 2.25, 1.78, etc. There is no common ratio, and so it is not a geometric sequence.

This sequence is given by\[\left\{ n^2 \right\}_{n = 1}^{\infty}\]It is a power sequence.