Question

已知等比数列｛an}中,公比q=2,且a1*a2*a3...a30=2^30,则a3*a6*a9...a30=

Answer 1

a1*a2*a3...a30=a1^30*q^(1+2+3+…+29)=a1^30*2^(15*29)=[a1^10*2^(5*29)]^3=2^30

a1^10*2^(5*29)=2^10

a3*a6*a9...a30=a1^10*q^(2+5+8+…+29)=a1^10*2^(5*31)=[a1^10*2^(5*29)]*2^10=2^10*2^10=2^20