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 Sn; (2) prove that sequence {an} is arithmetic sequence | Math enthusiast | Mathematical art

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 Sn; (2) prove that sequence {an} is arithmetic sequence

1. S1 = A1 = - 2, S2 = a1 + A2 = - 2 + 2 = 0, S3 = a1 + A2 + a3 = - 2 + 2 + 6 = 6, let Sn = Mn & # 178; + BN + C (m ≠ 0) n = 1, S1 = - 2; n = 2, Sn = 0; n = 3, Sn = 6 substitute m + B + C = - 2 (1) 4m + 2B + C = 0 (2) 9m + 3B + C = 6 (3) respectively to get m = 2B = - 4, C = 0sn = 2n & # 178; - 4n2. N ≥ 4, Sn = 2n & # 178; - 4N

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