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

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

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

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