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答案是1/4？！不好意思，我看错了，看成了A3/A6了:Sn=[n(A1+An)]/2 =nA1+[n(n-1)d]/2s3=3a1+3ds6=6a1+15ds12=12a1+66ds3/s6=(3a1+3d)/(6a1+15d)=1/4解得d=2a1s6/s12=(6a1+15d)/(12a1+66d)=36a1/144a1=1/4