已知等比数列{an}各项均为正数,数列{bn}满足bn=log2^an,b1+b2+b3=3,b1b2b3=-3,求an
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解决时间 2021-03-06 11:47
- 提问者网友：辞取
- 2021-03-05 22:40
已知等比数列{an}各项均为正数,数列{bn}满足bn=log2^an,b1+b2+b3=3,b1b2b3=-3,求an
最佳答案
- 五星知识达人网友：佘樂
- 2021-03-05 22:59
a1,q
b1=log2a1
b2=log2a2=loga1+log2q
b3=log2a3=log2a1q^2=log2a1+2log2q
相加得log2a1q=log2a2=1
a2=a1q=2 log2a1=x log2a1q^2=2-x
b1*b2*b3=x*1*(x-2)=-3
x=1 or
x=-3
代入就是了
b1=log2a1
b2=log2a2=loga1+log2q
b3=log2a3=log2a1q^2=log2a1+2log2q
相加得log2a1q=log2a2=1
a2=a1q=2 log2a1=x log2a1q^2=2-x
b1*b2*b3=x*1*(x-2)=-3
x=1 or
x=-3
代入就是了
全部回答
- 1楼网友：青尢
- 2021-03-06 01:26
不可能吧，你打错了
- 2楼网友：山君与见山
- 2021-03-06 00:31
b1+b2+b3=3由题意得log2^a1+log2^a2+log2^a3=log2^(a1*a2*a3)=3=log2^8 得a1*a2*a3=8又因为数列{an}为等比数列
根据其性质，a1*a2*a3=8=a2^3，a2=2,由b1b2b3=-3设等比为q得,log2^a1*log2^a2*log2^a3=log2^(a2/q)*log2^(a2*q)=-3得(log2^a2-log2^q)*(log2^a2+log2^q)=1-log2^(q*q)=1-2log2^q=-3,即2log2^q=4,得log2^q=2,q=4又因为等比数列{an}各项均为正数所an=a2*q^(n-2)=2*2^9n-2)=2^(n-1)
根据其性质，a1*a2*a3=8=a2^3，a2=2,由b1b2b3=-3设等比为q得,log2^a1*log2^a2*log2^a3=log2^(a2/q)*log2^(a2*q)=-3得(log2^a2-log2^q)*(log2^a2+log2^q)=1-log2^(q*q)=1-2log2^q=-3,即2log2^q=4,得log2^q=2,q=4又因为等比数列{an}各项均为正数所an=a2*q^(n-2)=2*2^9n-2)=2^(n-1)
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