Answer:
(c) Neither
Step-by-step explanation:
You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....
The first differences of terms of this sequence are ...
7 -2 = 5
14 -7 = 7
23 -14 = 9
34 -23 = 11
These difference are not constant, so the sequence is not arithmetic.
These differences do not have a common ratio, so the sequence is not geometric.
However, these differences do have a common difference:
7 -5 = 2
9 -7 = 2
11 -9 = 2
The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.
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Additional comment
The sequence is described by the quadratic equation ...
a(n) = n² +2n -1