等差数列an,公差d不等于0,a1 a3 a4 等比 求(a1+a3+a9)/(a2+a4+a10)

等差数列an,公差d不等于0,a1 a3 a4 等比 求(a1+a3+a9)/(a2+a4+a10)
等差数列an,公差d不等于0,a1 a3 a4 等比 求(a1+a3+a9)/(a2+a4+a10)

等差数列an,公差d不等于0,a1 a3 a4 等比 求(a1+a3+a9)/(a2+a4+a10)
等比a3²=a1a4
(a1+2d)²=a1(a1+3d)
a1d+4d²=0
d≠0
a1=-4d
所以原式=(a1+a1+2d+a1+8d)/(a1+d+a1+3d+a1+9d)
=(3a1+10d)/(3a1+13d)
=(-12d+10d)/(-12d+13d)
=-2

等比数列定义知，an=a1*q^(n-1)。
所以，a3=a1*q^2;a9=a1*q^8;a2=a1*q;a4=a1*q^3;a10=a1*q^9
代入，(a1(1+q^2+q^8))/(a1*q(1+q^2+q^8))=1/q
答案就是1/q