Question

设Sn是等差数列{an}的前n项和,若S3比S6=1比3,求S6比S12=

Answer 1

设等差数列首项为a，公差为d:
S3=3a+3d
S6=6a+15d
S12=12a+66d
由题意：
S3/S6=1/3
即：(3a+3d)/(6a+15d)=1/3
解得：a=2d
∴S6/S12
=(6a+15d)/(12a+66d)
=27d/90d
=27/90
=3/10

Answer 2

首先你要知道等差数列的顺次n项和性质
即sn,s2n-sn,s3n-s2n成公差为n²d的等差数列
则s6-s3=s3+9d
由s3/s6得s3=9d
则s6=27d
d=s6/27
s9-s6=s6-s3+9d得s9=2s6
s12-s9=s9-s6+9d得s12=3s6+9d
得s6/s12=s6/(3s6+s6/3)=3/10