Given that the first term of the arithmetic sequence A1 = 25, and S9 = S17, ask what is the value of N, and what is the maximum value of Sn?

Given that the first term of the arithmetic sequence A1 = 25, and S9 = S17, ask what is the value of N, and what is the maximum value of Sn?

S9 = s17sn = Na1 + [n (n-1) / 2] D9 * 25 + 36d = 17 * 25 + 17 * 8 * d225 + 36d = 425 + 136d100d = - 200D = - 2An = a1 + (n-1) d = 25-2 (n-1) = 27-2n (n belongs to n *) Sn = n (a1 + an) / 2 = n (25 + 27-2n) / 2 = [52n-2n ^ 2] / 2 = 26n-n ^ 2 = - (N-13) ^ 2 + 169

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