设{an}是由正数组成的等比数列,公比q=2,且a1×a2×a3×…×a30=2³º,那么a3×a6×a9×…×a30=?
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![设{an}是由正数组成的等比数列,公比q=2,且a1×a2×a3×…×a30=2³º,那么a3×a6×a9×…×a30=?](/uploads/image/z/11428083-27-3.jpg?t=%E8%AE%BE%7Ban%7D%E6%98%AF%E7%94%B1%E6%AD%A3%E6%95%B0%E7%BB%84%E6%88%90%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%85%AC%E6%AF%94q%3D2%2C%E4%B8%94a1%C3%97a2%C3%97a3%C3%97%E2%80%A6%C3%97a30%3D2%26%23179%3B%26%23186%3B%2C%E9%82%A3%E4%B9%88a3%C3%97a6%C3%97a9%C3%97%E2%80%A6%C3%97a30%3D%3F)
设{an}是由正数组成的等比数列,公比q=2,且a1×a2×a3×…×a30=2³º,那么a3×a6×a9×…×a30=?
设{an}是由正数组成的等比数列,
公比q=2,且a1×a2×a3×…×a30=2³º,那么a3×a6×a9×…×a30=?
设{an}是由正数组成的等比数列,公比q=2,且a1×a2×a3×…×a30=2³º,那么a3×a6×a9×…×a30=?
a1a2a3……a30=(a1a4a7……a28)(a2a5a8……a29)(a3a6a9……a30)
a2=2a1,a5=2a4,a8=2a7,a29=2a28
a3=4a1,a6=4a4,a9=4a7,a30=4a28
于是(a1a4a7……a28)(a1a4a7……a28*2^10)(a1a4a7……a28*4^10)=2^30
得a1a4a7……a28=1
于是a3a6a9……a30=a1a4a7……a28*4^10=2^20
a1×a2×a3×…×a30
=(a3/q²)×(a2/q)×a3×(a6/q²)×(a6/q)×a6×........×(a30/q²)×(a30/q)×a30
=(a3×a6×a9×…×a30)³/q³º
∴ (a3×a6×a9×…×a30)³/q³º=2³&...
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a1×a2×a3×…×a30
=(a3/q²)×(a2/q)×a3×(a6/q²)×(a6/q)×a6×........×(a30/q²)×(a30/q)×a30
=(a3×a6×a9×…×a30)³/q³º
∴ (a3×a6×a9×…×a30)³/q³º=2³º
∴ (a3×a6×a9×…×a30)³=2³º×2³º
∴ a3×a6×a9×…×a30=2²º
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