Given that the first term A1 of the arithmetic sequence {an} is less than 0, the tolerance D ≠ 0, and the absolute value A4 = the absolute value A12, if the first n terms and Sn get the minimum value, then n= I made a mistake!

Given that the first term A1 of the arithmetic sequence {an} is less than 0, the tolerance D ≠ 0, and the absolute value A4 = the absolute value A12, if the first n terms and Sn get the minimum value, then n= I made a mistake!

It should be n = 7 or 8
Because A8 = 0, S7 = S8

It is known that the sum of the first n terms of the arithmetic sequence is Sn, and S13 < 0, S12 > 0, then the term with the smallest absolute value in the sequence is ()
A. Item 5 B. item 6 C. item 7 d. item 8

∵ S13 = 13 (a1 + A13) 2 = 13 × 2a72 = 13a7 ＜ 0, S12 = 12 (a1 + A12) 2 = 12 (A6 + A7) 2 = 6 (A6 + A7) ＞ 0 ∵ A6 + A7 ＞ 0, a7 ＜ 0, | A6 | - | A7 | = A6 + A7 ＞ 0, | A6 | > | A7 | the term with the smallest absolute value in the sequence {an} is A7, so C is selected

It is known that the sum of the first n terms of the arithmetic sequence is Sn, and S13 < 0, S12 > 0, then the term with the smallest absolute value in the sequence is ()
A. Item 5 B. item 6 C. item 7 d. item 8

∵ S13 = 13 (a1 + A13) 2 = 13 × 2a72 = 13a7 ＜ 0, S12 = 12 (a1 + A12) 2 = 12 (A6 + A7) 2 = 6 (A6 + A7) ＞ 0 ∵ A6 + A7 ＞ 0, a7 ＜ 0, | A6 | - | A7 | = A6 + A7 ＞ 0, | A6 | > | A7 | the term with the smallest absolute value in the sequence {an} is A7, so C is selected