Question

an是由正数组成的等比数列,公比q≠1,且a2,a3/2,a1成等差数列

Answer 1

an=a1*q^(n-1)

q≠1,

a2+a1=a3,

a1q+a1=a1*q^2,

1+q=q^2,

q^2-q-1=0,

q=(1+√5)/2,q=(1-√5)/2,

an是由正数组成的等比数列(q=(1+√5)/2)

a3+a4=a1(q^2+q^3)

a4+a5=a1(q^3+q^4)

(a3+a4)/(a4+a5)

=a1(q^2+q^3)/a1(q^3+q^4)

=1/q=2/(1+√5)=√5-1