Question

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

Answer 1

a1=a3-2d，a9=a3+6d
因为a1,a3,a9成等比数列，所以有
(a3)^2=(a1)*(a9)
所以(a3)^2=(a3-2d)(a3+6d)
所以3d^2=d*(a3)
因为d不等于0
所以a3=3d
所以
(a1+a3+a9)/(a2+a4+a10)
=[(a3-2d)+a3+(a3+6d)]/[(a3-d)+(a3+d)+(a3+7d)]
=[3(a3)+4d]/[3(a3)+7d]
=[9d+4d]/[9d+7d]
=[13d]/[16d]
=13/16