已知等比数列{an}的公比q≠1,且akak+1ak+2ak+3ak+4=a6a8a12a16a18,那么k等于

Question

已知等比数列{an}的公比q≠ 1,且akak+1ak+2ak+3ak+4= a6a8a12a16a18,那么k等于

Answer 1

a(k)*a(k+1)*a(k+2)*a(k+3)*a(k+4)= a6*a8*a12*a16*a18
a(k)*a(k)*q*a(k)*q^2*(a(k)*q^3*a(k)*q^4=a(6)*a(6)*q^2*a(6)*q6*a(6)*q^10*a(6)*q^12
a(k)^5*q^10=a(6)^5*q^30
a(k)^5=a(6)^5*q^20
[a1*q^(k-1)]^5=(a1*q^5)^5*q^20
q^(5k-5)=q^45
k=10