Answer:
No, the sequence neither has a common difference or a common ratio. The sequence is the list of perfect squares.
Step-by-step explanation:
You are right that is neither.
For it to be arithmetic you must have a common difference. That is, a chosen term minus it's previous term has to be the same number no matter the pair.
Let's look at that:
4-1=3
9-4=4
16-9=7
25-16=9
36-25=11
These are definitely not the same difference so there is no common difference which means the sequence is not arithmetic. We could have stopped at the first two since those differences weren't even the same.
For it to be geometric you must have a common ratio. That is, a chosen term divided by it's previous term must be the same number no matter the pair.
Let's look at that:
4/1=4
9/4=2.25
16/9=1.777777777777777(repeating)
25/16=1.5625
36/25=1.44
These are definitely not the same ratio so there is no common ratio which means the sequence is not geometric. We didn't have to find all of the ratios. We could have stopped at first two and said yep not geometric because the first two weren't even the same.
The list you have here is actually the sequence of perfect squares.
