Question

各项均正的等比数列{an}中，a1a2……a18=2^18 若公比q=2,求a3a6a9a12a15a18的值

Answer 1

解：
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
不明白请追问。

Answer 2

a3a6a9a12a15a18=a1a2a3a4a5a6*q^(2*6)
a1a2……a18=a1a2a3a4a5a6*a1a2a3a4a5a6*q^6*a1a2a3a4a5a6*q^(2*6)
=(a1a2a3a4a5a6)^3*q^(3*6)=2^18
a1a2a3a4a5a6=1
a3a6a9a12a15a18=2^12