Determine whether the sequence is arithmetic, geometric, both, or neither. 1, 4, 9, 16, 25, . . .
Mathematics · High School · Thu Feb 04 2021
Answered on
Given the sequence:
1, 4, 9, 16, 25
Determine if the numbers are geometric, arithmetic, both or neither.
Solution:
In order to determine if the sequence is arithmetic we find for the common difference, hence, it can be seen that the numbers are increasing with different values, therefore we can assume that the sequence is not an arithmetic sequence.
In order to determine if the sequece is geometric, we simply need to find the common ratio. To do so we divide the first term to the second term, then the second term to the 3rd term and compare if they are the same.
= 4/1
= 4
= 9/4
=2.25
It can be seen that the given sequence is not geometric.
Final answer:
Neither arithmetic or geometric.