数列an是等差数列,a1,a2,a3成等比数列.则a1+a3+a9/a2+a4+a10等于多少?

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数列an是等差数列,a1,a2,a3成等比数列.则a1+a3+a9/a2+a4+a10等于多少?

数列an是等差数列,a1,a2,a3成等比数列.则a1+a3+a9/a2+a4+a10等于多少?
数列an是等差数列,a1,a2,a3成等比数列.则a1+a3+a9/a2+a4+a10等于多少?

数列an是等差数列,a1,a2,a3成等比数列.则a1+a3+a9/a2+a4+a10等于多少?
解;设首相为a
则a1=a,a3=a+2d,a9=a+8d,a2=a+d,a4=a+3d,a10=a+9d
a1,a3,a9成等比数列
(a+2d)^2=a*(a+8d)
a=d
所以(a1+a3+a9)/(a2+a4+a10)=(a+a+2d+a+8d)/(a+d+a+3d+a+9d)
=13a/16a=13/16

a2=a1+d,a3=a1+2d,由a1,a2,a3成等比数列,所以可推出a1*(a1+2d)=(a1+d)^2,所以d=0,所以a1=a3=a9=a2=a4=a10,所以答案为1/3

设等差d
a2=a1+d, a3=a1+2d
(a1+d)^2=a1(a1+2d)
2a1d+d^2=2a1d
d=0
an=a1
(a1+a3+a9)/(a2+a4+a10)=3a1/(3a1) =1