若等差数列中,S12=8S4,d≠0,则a1/d=?
问题描述：
若等差数列中,S12=8S4,d≠0,则a1/d=?
答
S12=a1+a12=(a1+a12)*6=[a1+a1+(12-1)*d]*6=(2a1+11d)*6
8S4=8*[(a1+a4)*2]=8*{[a1+a1+(4-1)*d]*2}=8*[(2a1+3d)*2]=16*(2a1+3d)
即(2a1+11d)*6=16*(2a1+3d),
(2a1+11d)*3=8*(2a1+3d),
6a1+33d=16a1+24d,
10a1=9d,a1/d=9/10