等比数列{an}公比为2.a1*a2*a3······a30=2的四十五次方,求a1*a4*a7···
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![等比数列{an}公比为2.a1*a2*a3······a30=2的四十五次方,求a1*a4*a7···](/uploads/image/z/7206163-43-3.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E5%85%AC%E6%AF%94%E4%B8%BA2.a1%2Aa2%2Aa3%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7a30%3D2%E7%9A%84%E5%9B%9B%E5%8D%81%E4%BA%94%E6%AC%A1%E6%96%B9%2C%E6%B1%82a1%2Aa4%2Aa7%C2%B7%C2%B7%C2%B7)
等比数列{an}公比为2.a1*a2*a3······a30=2的四十五次方,求a1*a4*a7···
等比数列{an}公比为2.a1*a2*a3······a30=2的四十五次方,求a1*a4*a7···
等比数列{an}公比为2.a1*a2*a3······a30=2的四十五次方,求a1*a4*a7···
a1*a2*a3······a30=(a1)^(30).(q)^(1+2+……+29)
=(a1)^(30).(q)^(435)
=2^(45)
因为q=2,代入可得:
(a1)^(30).2^(435)=2^(45)
得出:
a1=2^(-13)
a1*a4*a7=(a1)^3.(q)^9
=[2^(-13)]^3.2^(9)
=2^(-30)
an=a1*2^(n-1)
a1*a2*a3······a30=a1* (a1*2)*(a1*2^2)*……*(a1*2^29)
=a1^30*2^(1+2+……+29)
=a1^30*2*[(1+29)*29/2)]
...
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an=a1*2^(n-1)
a1*a2*a3······a30=a1* (a1*2)*(a1*2^2)*……*(a1*2^29)
=a1^30*2^(1+2+……+29)
=a1^30*2*[(1+29)*29/2)]
=a1^30*2^435=2^45
a1^30=2^(-390)
a1=2^(-13)
a1*a4*a7=2^(-13) *[2^(-13)*2^3]*[2^(-13)*2^6] =2^(-30)
收起
a1*a2*a3······a30=2的四十五次方
a1*a1q*a1q^2......a1q^29=2^45
q=2
a1=?
依次计算
条件不够啊 你后面的a1*a4*a7........到哪里呢?应该是一共三十项吧?
知道a1*a2*a3······a30=2的四十五次方,我能求出a1来
但我不知道你要求什么啊?
a1*a4*a7···后面总有个尽头吧?