已知等比数列{an}满足an>0,公比为q=2,若a1*a2*a3…a30=2的30次方,则a1a4a7…a28为多少

题目

已知等比数列{an}满足an>0,公比为q=2,若a1*a2*a3…a30=2的30次方,则a1a4a7…a28为多少

答案

(a1a4a7…a28)^3
= a1a1a1a4a4a4a7a7a7...a28a28a28
= a1a2/qa3/q/qa4a5/qa6/q/q.a28a29/qa30/q/q
= a1a2a3a4...a29a30/(q^30)
= 2^30/(2^30)
= 1
故 a1a4a7…a28 = 1