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?

1 Answer
Feb 17, 2017

Answer:

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!