In the arithmetic sequence {an}, A1 = - 60, A17 = - 12. (1) find the general term an, (2) find the sum of the first 30 terms of the sequence | Math enthusiast | Mathematical art

In the arithmetic sequence {an}, A1 = - 60, A17 = - 12. (1) find the general term an, (2) find the sum of the first 30 terms of the sequence

(1) Let the tolerance of the arithmetic sequence be d. from the meaning of the question, we can get: A17 = a1 + 16d, that is - 12 = - 60 + 16d, we can get d = 3, ｜ an = - 60 + 3 (n-1) = 3n-63. (2) from (1), we can know that an = 3n-63, A30 = 27, so the sum of the first 30 items of the sequence is: S30 = 30 × (− 60 + 27) 2 = - 495

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