She is incorrect. The sequence is neither arithmetic nor geometric.
Why isn't it arithmetic? Because the distance from 2 to 3 is different from 3 to 5
we add 1 to go from 2 to 3
we add 2 to go from 3 to 5
Put another way,
3-2 = 1
5-3 = 2
This shows that there is no common difference. Therefore this sequence isn't arithmetic
----------------------------------
There is no common ratio as well. Pick any term and divide by its previous term
(term2)/(term1) = 3/2 = 1.5
(term3)/(term2) = 5/3 = 1.67
(term4)/(term3) = 8/5 = 1.6
The results are close, but not the exact same every time. The inconsistent results above show there isn't any common ratio. This shows us we don't have a geometric sequence.
Note: this sequence is very close to a subset of the Fibonacci sequence (if the 12 was 13, then it would work perfect)
