Question

等差数列{An}的公差为d(d不为0),且A1,A3,A9成等比数列，求(A1+A3+A9)/(A2+A4+A10)的值

文字表达：问第一、三、九项的和，除以第二、四、十项的和，结果是多少？

Answer 1

1, A1/A3=A3/A9 ==>
A1*A9=A3*A3 ==>
A1*(A1+8d)=(A1+2d)(A1+2d) ==>
A1=d

so
(A1+A3+A9)/(A2+A4+A10) =
(A1+A1+2d+A1+8d)/(A1+d+A1+3d+A1+9d)=
13d/16d=13/16

Answer 2

A1=1,A3=3,A9=9
其实就是以1为首项，公差为1的等差数列

结果是 13/16

Answer 3

(A1+A3+A9)/(A2+A4+A10)＝13／16