Question

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

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

麻烦讲解详细过程

Answer 1

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=16a1
所以(a1+a3+a9)/(a2+a4+a10)=13/16

C

Answer 2

因为a1,a3,a9成等比数列
所以(a1+2d)^2=a1(a1+8d)

解得a1=d

（a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13/16

选C

Answer 3

C

因为a1,a3,a9成等比数列

(a1+2d)^2=a1(a1+8d)
d≠0
（a1+a3+a9)/(a2+a4+a10)=(3a1+10d)/(3a1+13d)=13/16

C