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

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 {an} is Sn, if S12 > 0, S13

S12=6(a6+a7)>0 a6+a7>0 S13=13*a7-a7
The smallest absolute value is item 7

The sum of the first n terms of the arithmetic sequence is SN. If S130, the term with the smallest absolute value in the sequence is SN

The sum of the first n terms of the sequence {an} is Sn, if S130,
Tolerance D ＜ 0
a1>0
Sequence must be decreasing sequence
s12=(a1+a12)*12/2>0
a1+a12>0
S13=(a1+a13)*13/2