Given that the general term formula of sequence is an = 2n-47, then when Sn takes the minimum value, n=______ ．

Given that the general term formula of sequence is an = 2n-47, then when Sn takes the minimum value, n=______ ．

According to the meaning of the question, an = 2n-47, so {an} is an arithmetic sequence with the first term of - 45 and the tolerance of 2, then Sn = n (− 45 + 2n − 47) 2 = n2-46n = (n-23) 2-529, combined with the properties of quadratic function, when n = 23, Sn has the minimum value, so the answer is: 23

In the sequence {an}, an + 1 + an = 2n-44 (n ∈ n *,) A1 = - 23 (1) find an; (2) let Sn be the sum of the first n terms of {an}, find the minimum value of Sn

(1) ∵ an + 1 + an = 2n-44, ① ∵ an + 2 + an + 1 = 2 (n + 1) - 44, ② - ① get an + 2-An = 2, in ∵ sequence {an}, the odd term constitutes the arithmetic sequence, the even term constitutes the arithmetic sequence, and the tolerance is 2. It is known that a1 + A2 = 2-44 = - 42, A2 = - 19, when n is odd, an = a1 + (n + 12 − 1) × 2 = n-24