It is known that the first n terms and Sn of sequence {an} are quadratic functions of N, and A1 = - 2, A2 = 2, A3 = 6. (1) find the expression of Sn; (2) find the general term an

It is known that the first n terms and Sn of sequence {an} are quadratic functions of N, and A1 = - 2, A2 = 2, A3 = 6. (1) find the expression of Sn; (2) find the general term an

(1) Let Sn = AX2 + BX + C (a ≠ 0). ∵ A1 = - 2, A2 = 2, A3 = 6. ∵ 2 = a + B + C − 2 + 2 = 4A + 2B + C − 2 + 2 + 6 = 9A + 3B + C. A = 2B = - 4C = 0 ∵ Sn = 2n2 − 4N. (2) ∵ A1 = S1 = 2-4 = - 2. When n ≥ 2, an = sn-sn-1 = 2n2-4n - [2 (n-1) 2-4 (n-1)] = 4n-6