已知等差数列{an}的公差d不等于0且a1,a4,a8成等比数列,则﹙a1+a4+a8)／﹙a2+a5+a9)=

题目

已知等差数列{an}的公差d不等于0且a1,a4,a8成等比数列,则﹙a1+a4+a8)／﹙a2+a5+a9)=

答案

a4=a1 +3d,a8=a1+7d
a1,a4,a8成等比数列,a4²=a1×a8
(a1 +3d)²=a1×(a1+7d)
整理得,a1=9d
所以an=a1+(n-1)d=(n+8)d
﹙a1+a4+a8)／﹙a2+a5+a9)=(9d+12d+16d)/(10d+13d+17d)=37/40