已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*a30=2^45则a1*a4*a7*…*a28=已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*an=2^45则a1*a4*a7*…*a28=
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![已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*a30=2^45则a1*a4*a7*…*a28=已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*an=2^45则a1*a4*a7*…*a28=](/uploads/image/z/4020040-64-0.jpg?t=%E5%B7%B2%E7%9F%A5%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%7Ban%7D%E4%B8%AD%E5%85%AC%E6%AF%94q%3D2%2Ca1%2Aa2%2Aa3%2A%E2%80%A6%2Aa30%3D2%5E45%E5%88%99a1%2Aa4%2Aa7%2A%E2%80%A6%2Aa28%3D%E5%B7%B2%E7%9F%A5%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%7Ban%7D%E4%B8%AD%E5%85%AC%E6%AF%94q%3D2%2Ca1%2Aa2%2Aa3%2A%E2%80%A6%2Aan%3D2%5E45%E5%88%99a1%2Aa4%2Aa7%2A%E2%80%A6%2Aa28%3D)
已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*a30=2^45则a1*a4*a7*…*a28=已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*an=2^45则a1*a4*a7*…*a28=
已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*a30=2^45则a1*a4*a7*…*a28=
已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*an=2^45则a1*a4*a7*…*a28=
已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*a30=2^45则a1*a4*a7*…*a28=已知由正数组成的等比数列{an}中公比q=2,a1*a2*a3*…*an=2^45则a1*a4*a7*…*a28=
原题印刷错误
a1*a2*a3*…*a30=a1*(a1*q)*(a1*q^2)…*(a1*q^29)=a1^30*q^(1+2+…29)=a1^30*q^435=2^45
所以a1^30=2^45/2^435 所以a1^10=1/2^130
a1*a4*a7*…*a28=a1*(a1*q^3)*(a1*q^6)*(a1*q^6)…*(a1*q^27)=a1^10*q^(1+4+7+10+13...
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a1*a2*a3*…*a30=a1*(a1*q)*(a1*q^2)…*(a1*q^29)=a1^30*q^(1+2+…29)=a1^30*q^435=2^45
所以a1^30=2^45/2^435 所以a1^10=1/2^130
a1*a4*a7*…*a28=a1*(a1*q^3)*(a1*q^6)*(a1*q^6)…*(a1*q^27)=a1^10*q^(1+4+7+10+13+16+19+22+25+28)=a1^10*2^145=2^15
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a1*a2*a3*…*a30=2^45可转化为(a15a16)^15=2^45,又因为a15=a16/2,所以a16=4,
a1*a4*a7*…*a28=(a13a16)^5=(1/2×4)^5=2^5
an*a(n+1)*a(n+2)
=an*(an*q)*(an*q²)
=(an)³*q³
a1*a2*a3*……*a30
=(a1*a2*a3)*(a4*a5*a6)*……*(a28*a29*a30)
=[(a1)³*q³]*[(a4)³*q³]*……*[(a28)³...
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an*a(n+1)*a(n+2)
=an*(an*q)*(an*q²)
=(an)³*q³
a1*a2*a3*……*a30
=(a1*a2*a3)*(a4*a5*a6)*……*(a28*a29*a30)
=[(a1)³*q³]*[(a4)³*q³]*……*[(a28)³*q³]
=(a1*a4*a7*……*a28)³*q^30
=(a1*a4*a7*……*a28)³*2^30
=2^45
a1*a4*a7*……*a28
=(2^45/2^30)^(1/3)
=2^5
=32
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