Question

设等差数列{an}的前n项和为Sn,已知a3=12,S12>0,S13<0.

(1)求公差d的取值范围.

(2)求{an}前n项和Sn最大时n的值.

 

Answer 1

(1) -<d<-3 (2)6

【解析】(1)∵S12>0,S13<0,

∴

∴-<d<-3.

(2)由S13==13a7<0,知a7<0,

S12=6(a1+a12)=6(a6+a7)>0,知a6>0,

又∵d<0,∴n≤6时,an>0,n≥7时,an<0,

∴S6最大,∴n=6.