Question

等比数列an a1大于0 a2a4+2a3a5+a4a6=9 a3+a5=

Answer 1

a(n)=aq^(n-1),a>0.

9=a(2)a(4)+2a(3)a(5)+a(4)a(6)=a^2[q^4+2q^6+q^8]=a^2q^4[1+2q^2+q^4]=[aq^2(1+q^2)]^2,

aq^2(1+q^2)=3,

a(3)+a(5)=a[q^2+q^4]=aq^2(1+q^2)=3