设Sn是等差数列{an}的前n项和,若S3/S6=1/4,则S6/S12等于?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/25 20:41:35

设等差数列的首项为a1,公差为d.
则有（a1+2d）/(a1+5d)=1/4,解得d=-a1
那么S6/S12=（a1+5d）/(a1+11d)=(-4a1)/(-10a1)=2/5
再问：答案是1/4？！
再答：不好意思，我看错了，看成了A3/A6了 :Sn=[n(A1+An)]/2 =nA1+[n(n-1)d]/2 s3=3a1+3d s6=6a1+15d s12=12a1+66d s3/s6=(3a1+3d)/(6a1+15d)=1/4 解得d=2a1 s6/s12=(6a1+15d)/(12a1+66d)=36a1/144a1=1/4

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