问题 填空题
设Sn是等差数列{an}的前n项和,若
S3
S6
=
1
3
,则
S6
S12
=______.
答案

由等差数列的性质可得S3,S6-S3,S9-S6,S12-S9成等差数列,

S3
S6
=
1
3
可得S6=3S3,故S6-S3=2S3

故S9-S6=3S3,S12-S9=4S3

解之可得S9=6S3,S12=10S3

S6
S12
=
3S3
10S3
=
3
10

故答案为:

3
10

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