Question

设等差数列{an}的前n项和为Sn,若S6/S3=3,则S9/S6=？

Answer 1

易知，S3，S6-S3，S9-S6成等差数列，所以
S3+S9-S6=2(S6-S3)
S9=3(S6-S3)
又 S6/S3=3，S3=S6/3
所以 S9=3(S6-S6/3)=2S6
S9/S6=2

Answer 2

设公差为d则
sn=n(2a1+(n-1)d)/2
s6/s3=6(2a1+5d)/3(2a1+2d)=(2a1+5d)/(a1+d)=3
所以2a1+5d＝3(a1+d)
a1=2d
s9/s6=9(2a1+8d)/6(2a1+5d)=3(a1+4d)/(2a1+5d)=3*6d/9d=2