已知各项都为正数的等比数列{an}中,公比a1a2a3a4...a29a30=5^30,求a3a6a9...a30=?

问题描述:

已知各项都为正数的等比数列{an}中,公比a1a2a3a4...a29a30=5^30,求a3a6a9...a30=?

a1*a2*a3=a2^3,a3=a2*q,a3=(a1*a2*a3)^(1/3)*q
a6=(a4*a5*a6)^(1/3)*q
a9=(a7*a8*a9)^(1/3)*q
……
a3a6a9...a30
=(a1a2a3a4...a29a30)^(1/3)*q^10
=5^10*q^10
把q代入