若等差数列{AN}的公差D不等于0 且A1,A3,A7成等比数列,A1分之A2等于

问题描述:

若等差数列{AN}的公差D不等于0 且A1,A3,A7成等比数列,A1分之A2等于

a1(a1+6d)=(a1+2d)²
a1²+6a1d=a²+4a1d+4d²
d=5a1/2
a2/a1=(a1+5a1/2)/a1=7/2

a3^2=(a3-2d)*(a3+4d)=a3^2+2da3-8d^2
a3=4d
a1=2d
a2=3d
所以a1分之a2=3/2