设{an}是由正数组成的等比数列,公比q=2,且a1a2a3…a30=2^30,则a3a6a9…a30= [ ]
设{an}是由正数组成的等比数列,公比q=2,且a1a2a3…a30=2^30,则a3a6a9…a30= [ ]
人气:458 ℃ 时间:2020-05-25 08:28:33
解答
由a1a2a3…a20=2^30,q=2可知:
a1a2a3¨a30=2^30
a1a2a3¨a30=a1^30q^(1+2+…+29)
=a1^30q^(29×15)
=a1^30q^435
=a1^30×2^435
=a1^30×2^435
=2^30
所以
a1^30=1/2^405
所以a1^10=1/2^135………………(二边开立方)
a3a6a9…a30
=a1^10q^(2+5+…+29)
=a1^10q^(31×5)
=a1^10q^155
=a1^10×2^155
=1/2^135×2^155
=2^20
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