Question

已知等比数列{an}各项均为正数且a1,二分之一a3,a2成等差数列则a4+a5分之a3+a4等于

Answer 1

设公比为q,首项为a1,则由a1,二分之一a3,a2成等差数列可得/

a3=a1+a2 即a1*q^2=a1+a1*q

q^2=1+q 可求得q=(1+√5)/2

(a3+a2)/(a4+a5)

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

=(q+1)/(q^2+q)

=1/q

=2/(1+√5)

=(√5-1)/2

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