各项均正的等比数列{an}中,a1a2……a18=2^18 若公比q=2,求a3a6a9a12a15a18的值
问题描述：
各项均正的等比数列{an}中,a1a2……a18=2^18 若公比q=2,求a3a6a9a12a15a18的值
答
a1a2……a18=2^18
=a1a4a7a10a13a16*a2a5a8a11a14a17*a3a6a9a12a15a18
=(a3a6a9a12a15a18)/(q^2)^6*(a3a6a9a12a15a18)/q^6*(a3a6a9a12a15a18)
=(a3a6a9a12a15a18)^3/q^18=(a3a6a9a12a15a18)^3/2^18
故(a3a6a9a12a15a18)^3=2^18*2^18=2^36
故a3a6a9a12a15a18=(2^36)^(1/3)=2^12