U need to prove it's an AP, not assume it is an AP and solve it
using the method of AP.
To prove you need to have values of S1, S2, S3 and so on and see what is the
pattern like.
As papercut87 has pointed out, it's a sequence, however, may I add
that this could be a better way to prove and solve:
Given Sn = pn + qn²,
Sn+1 = p(n+1) + q(n+1)² =
pn+qn² + (p + 2qn + q)
Sn+2 = ... = pn+qn² + (2p
+ 4qn + 4q)
Sn+3 = ... = pn+qn² + (3p
+ 6qn + 9q)
If u take the difference bet Sn+3 and Sn+2 u get a difference of (p + 2qn +
5q), and for Sn+2 and
Sn+1 u get a difference of
(p + 2qn + 3q)
Those are the terms of T3
and T2 respectively.
And from observation, first term is 2q and difference is p+q.
