Question

设等差数列{an}的前n项和为Sn，已知a3=12,s12>0,s13<0求公差d的取值范围

Answer 1

设公差为d
S12=(a3+a10)*6=(2a3+7d)*6=(24+7d)*6>0
S13=a7*13=(a3+4d)*13=(12+4d)*13<0
即24+7d>0且12+4d<0
解得-24/7<d<-3

Answer 2

因为s12>0, (a3-2d+a3-2d+11d)x12/2>0 s13<0, (a3-2d+a3-2d+12d)x13/2<0-24/7<d<-3

Answer 3

a3=a1+2d=12 a1=12-2dS12=12a1+66d>0 144-24d+66d>0 42d>-144 d>-24/7S13=13a1+78d<0 156-26d+78d<0 52d<-156 d<-3-24/7 <d<-3