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In the arithmetic sequence {an}, A1 = 3, the sum of the first n terms is Sn, the items of the arithmetic sequence {BN} are all positive, B1 = 1, the common ratio is Q, and B2 + S2 = 12, q = s2b2. (1) find an and BN; (2) let the sequence {CN} satisfy the first n terms and TN of CN = 1sn, {CN}, and prove that TN < 23
(1) ∵ in the arithmetic sequence {an}, A1 = 3, the sum of the first n terms is Sn, each item of the arithmetic sequence {BN} is positive, B1 = 1, the common ratio is Q, and B2 + S2 = 12, q = s2b2. ∵ Q + 3 + A2 = 12q = 3 + a1q, the solution is q = 3 or q = - 4 (rounding), ∵ A2 = 6, d = a2-a1 = 6-3 = 3, ∵ an = 3 + (n-1) · 3 = 3nbn = 3N
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