Question

已知{an}是等比数列,各项为正,且有a2*a4+2*a3*a5+a4*a6=25

Answer 1

设an=aq^n

a2*a4+2*a3*a5+a4*a6=25

aq^2*aq^4+2aq^3*aq^5+aq^4*aq^6=25

a^2q^6+2a^2q^8+a^2q^10=25

(aq^3)^2+2*aq^3*aq^5+(aq^5)^2=25

(aq^3+aq^5)^2=25

(aq^3+aq^5) =5