等比数列an的各项均为正数,且a1,1/2a3,a2乘等差数列则(a3+a4)÷（a4+a5）=

Question

等比数列an的各项均为正数,且a1,1/2a3,a2乘等差数列则(a3+a4)÷（a4+a5）=

Answer 1

an=a1q^(n-1)
a1,(1/2)a3,a2:等差数列
=> a2-(1/2)a3 = (1/2)a3-a1
a1(q-(1/2)q^2)= a1((1/2)q^2-1)
q-(1/2)q^2= (1/2)q^2-1
q^2-q-1=0
q=(1+√5)/2
(a3+a4)/(a4+a5)
=a1(q^2+q^3)/[a1(q^3+q^4)]
=1/q
=2/(1+√5)
=(√5-1)/2