已知等差数列{an}的公差d不等於0,且a1,a3,a9成等比数列,则（a1+a3+a9)/(a2+a4+a10)的值是

题目

已知等差数列{an}的公差d不等於0,且a1,a3,a9成等比数列,则（a1+a3+a9)/(a2+a4+a10)的值是
A.15/14
B.12/13
C.13/16
D.15/16

答案

a3=a1+2d q9=a1+8d a1,a3,a9成等比数列 所以(a1+2d)^2=a1*(a1+8d) a1^2+4a1d+4d^2=a1^2+8a1d d^2=a1d d≠0 d=a1 所以a1+a3+a9=a1+(a1+2d)+(a1+8d)=a1+3a1+9a1=13a1 a2+a4+a10=(a1+d)+(a1+3d)+(a1+9d)=2a1+4a1+10a1=1...