数列-设Sn是等差数列{an}的前n相和，若S3/S6=1/3,则S6/S12=?

来源：百度知道编辑：UC知道时间：2024/04/28 17:59:01

设Sn是等差数列{an}的前n相和，若S3/S6=1/3,则S6/S12=?

设等差数列首项为a，公差为d，可以计算出
S3=3a+3d
S6=6a+15d
S12=12a+66d

S3/S6=1/3
则（3a+3d）/（6a+15d）=1/3
解得a=2d
所以S6/S12=3/10

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等差数列S3,S6-S3,S9-S6,S12-S9也成等差数列
S3/S6=1/3,S6=3S3,S6-S3=2S3
S9-S6=3S3,S9=6S3
S12-S9=4S3,S12=10S3
所以S6/S12=3/10

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