2,3,5,8,12
dy=1,2,3,4 there is no common difference so this is not an arithmetic sequence.
2/1, 5/3, 8/5, 12/8 there is no common ratio so this is not a geometric sequence...
however,
d2y=1,1,1 which means that there is a constant acceleration, the sequence then is the result of a quadratic equation....
So we only need three equations to solve for a,b, and c of ax^2+bx+c=y
9a+3b+c=5, 4a+2b+c=3, a+b+c=2 getting differences...
5a+b=2, 3a+b=1 and again...
2a=1, so a=1/2 making 5a+b=2 become:
5/2+b=2, so b=-1/2 making a+b+c=2 become:
1/2-1/2+c=2, so c=2, thus the formula for the sequence is:
a(n)=(n^2-n+4)/2
So it is quadratic. It is not arithmetic or geometric.
