等比数列练习题,1、再等比数列{an}中,公比为q,a1+a2+a3=18,a2+a3+a4=-9,则a1比1-q为__
1个回答
1.(a1+a2+a3)/(a2+a3+a4)=a1(1+q+qq)/[a1qq(1+q+qq)=1/q=-2
q=-1/2
a1+a2+a3=a1(1+q+qq)=18
a1=-72
a1/(1-q)=-72/(1+1/2)=-48
2.因为a1=1/n,an=a1*q^(n-1),
所以a(n+2)=a1*q^(n+1)=(1/n)*q^(n+1)=n+1
即q^(n+1)=(n+1)*n
q1*q2*q3*……*qn=q^(1+2+3+……+n)=q^(1+n)*n/2
=[(n+1)*n]^1/2
＝根号下〔（n+1)*n〕
3.因为an=a1*q^(n-1),
a1=1,a的2n+2项＝2
所以
2=1*q^(2n+1)即q^(2n+1)=2
x1*x2*x3*……x2n
=q^1*q^2*q^3*……*q^2n
=q^(1+2+3+……+2n)
=q^[(1+2n)*2n/2]
=q^[n*(2n+1)]
=[q^(2n+1)]^n
=2^n
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