课时作业的的34等比数列的.doc
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- 2021-12-04 发布|
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课时作业34 等比数列
一、选择题
1.设数列{an}是等比数列,前n项和为Sn,假如S3=3a3,如此公比q为( )
A.-eq \f(1,2) B.1
C.-eq \f(1,2)或1 D.eq \f(1,4)
解析:当q=1时,满足S3=3a1=3a3.
当q≠1时,S3=eq \f(a1?1-q3?,1-q)=a1(1+q+q2)=3a1q2,解得q=-eq \f(1,2),综上q=-eq \f(1,2)或q=1.
答案:C
2.在等比数列{an}中,假如a4,a8是方程x2-3x+2=0的两根,如此a6的值是( )
A.±eq \r(2) B.-eq \r(2)
C.eq \r(2) D.±2
解析:由题意得a4a8=2,且a4+a8=3,如此a4>0,a8>0,又{an}为等比数列,故a4,a6,a8同号,且aeq \o\al(2,6)=a4a8=2,故a6=eq \r(2),选C.
答案:C
3.等比数列{an}的前n项和为Sn,且a1+a3=eq \f(5,2),a2+a4=eq \f(5,4),如此eq \f(Sn,an)=( )
A.4n-1 B.4n-1
C.2n-1 D.2n-1
解析:q=eq \f(a2+a4,a1+a3)=eq \f(1,2),如此eq \f(Sn,an)=eq \f(\f(a1[1-?\f(1,2)?n],1-\f(1,2)),a1?\f(1,2)?n-1)=2n-1.
答案:C
4.等比数列{an}中,对任意正整数n,a1+a2+a3+…+an=2n-1,如此aeq \o\al(2,1)+aeq \o\al(2,2)+aeq \o\al(2,3)+…+aeq \o\al(2,n)等于( )
A.eq \f(1,3)(4n-1) B.eq \f(1