设等差数列的前n项之和为Sn,已知a3=12,S12大于0,S13小于0,求公差d的取值范围 急

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设等差数列的前n项之和为Sn,已知a3=12,S12大于0,S13小于0,求公差d的取值范围 急
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设等差数列的前n项之和为Sn,已知a3=12,S12大于0,S13小于0,求公差d的取值范围 急
设等差数列的前n项之和为Sn,已知a3=12,S12大于0,S13小于0,求公差d的取值范围 急

设等差数列的前n项之和为Sn,已知a3=12,S12大于0,S13小于0,求公差d的取值范围 急
Sn=na1+n(n-1)d/2
S12=12a1+66d
S13=13a1+78d
又a3=a1+2d=12
a1=12-2d
S12=12(12-2d)+66d>0
S13=13(12-2d)+78d

S12=12a1+12×11d/2＞0,S13=13a1+13×12d/2＜0,∴ a1+5.5d＞0 ,a1+6d＜0
又 a3=a1+2d=12 ∴a1=12-2d ，代入上述两式中：12+3.5d＞0，12+4d＜0
∴-24/7＜d＜-3

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