Question

How do you determine whether the sequence `1^2, 2^2, 3^2, 4^2, 5^2,...` is arithmetic and if it is, what is the common difference?

Answer 1

No, it is not arithmetic.

Explanation:

This is not arithmetic. Arithmetic would mean that a number, `d` is added to each term. This would mean that the terms of the sequence would need to be equally spaced apart.

This is not the case here. The difference between `t_1` and `t_2` is `3`, and the difference between `t_2` and `t_3` is `5`. In fact, this series can be represented as

`t_n = n^2`

While an arithmetic sequence would be of the form

`t_n = a + (n - 1)d`

The sequence above can be modeled graphically as a parabola, while any arithmetic sequence would be a straight line.

Hopefully this helps!