Question

各项都是正数的等比数列 an中,3a1,1/2a3,2a2成等差数列,则(a2010+a2014)/(a2013+a20

Answer 1

3a1,1/2a3,2a2成等差数列

a3=a1q^2=3a1+2a1q、q^2-2q-3=0、q=-1(舍去)、q=3.

(a2010+a2014)/(a2013+a2011)

=(a2010*q+q^4*a2010)/(a2010*q^3+a2010*q)

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

=q(1+q^3)/q(1+q^2)

=1+q^3/1+q^2

=(1+8)/(1+4)

=9/5