Question

設(shè)等差數(shù)列{an}的前n項(xiàng)和為Sn,已知a3=12,S12>0,S13<0.

(1)求公差d的取值范圍.

(2)求{an}前n項(xiàng)和Sn最大時(shí)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時(shí),an>0,n≥7時(shí),an<0,

∴S6最大,∴n=6.