Let {an} have 3N items in total, and the sum of the first 2n items is 100, and the sum of the last 2n items is 200. Then what is the sum of the middle n items?

S2n = 100, A1 (1-Q ^ 2n) / (1-Q) = 100s3n Sn = 200, A1 (Q ^ n-q ^ 3n) / (1-Q) = 200, then q ^ n = 2s2n = 100 = A1 (1-Q ^ 2n) / (1-Q) = A1 (1 + Q ^ n) (1-Q ^ n) / (1-Q) = (1 + Q ^ n) Sn = 3Sn, so Sn = 100 / 3, middle n = 100-100 / 3

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