the sequence is arithmetic because the terms have a common difference.\nthe sequence is arithmetic because…

the sequence is arithmetic because the terms have a common difference.\nthe sequence is arithmetic because the terms do not have a common difference.\nthe sequence is not arithmetic because the terms have a common difference.\nthe sequence is not arithmetic because the terms do not have a common difference.

the sequence is arithmetic because the terms have a common difference.\nthe sequence is arithmetic because the terms do not have a common difference.\nthe sequence is not arithmetic because the terms have a common difference.\nthe sequence is not arithmetic because the terms do not have a common difference.

Answer

Explanation:

Step1: Recall arithmetic - sequence definition

An arithmetic sequence has a common difference (d=a_{n + 1}-a_{n}) for all (n).

Step2: Find differences between consecutive terms

For (n = 1), (a_1 = 1), (a_2=4), (d_1=a_2 - a_1=4 - 1=3). For (n = 2), (a_2 = 4), (a_3 = 9), (d_2=a_3 - a_2=9 - 4 = 5). Since (d_1\neq d_2), the terms do not have a common difference.

Answer:

The sequence is not arithmetic because the terms do not have a common difference.