高中数学数列练习题及解析 下载本文

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数列练习题

一.选择题(共16小题)

1.数列{an}的首项为3,{bn}为等差数列且bn=an+1﹣an(n∈N*),若b3=﹣2,b10=12,则a8=( ) A. 0 B. 3 C. 8 D. 11 2.在数列{an}中,a1=2,an+1=an+ln(1+),则an=( ) A. 2+lnn B. 2+(n﹣1)lnn C. 2+nlnn D. 1+n+lnn 3.已知数列{an}的前n项和Sn=n2﹣9n,第k项满足5<ak<8,则k等于( ) A. 9 B. 8 C. 7 D. 6 4.已知数列{an}的前n项和为Sn,a1=1,Sn=2an+1,则Sn=( ) A. 2n﹣1 B. C. D. 5.已知数列{an}满足a1=1,且an= A. an=B. ,且n∈N*),则数列{an}的通项公式为( ) C. an=n+2 D. an=(n+2)3n 6.已知数列{an}中,a1=2,an+1﹣2an=0,bn=log2an,那么数列{bn}的前10项和等于( ) A. 130 B. 120 C. 55 D. 50 7.在数列?an?中,若a1?1,an?1?2an?3(n?1),则该数列的通项an?( ) A. 2n?3 B. 2n?1?3 = +

C. 2n?3 D. 2n?1?3 8.在数列{an}中,若a1=1,a2=,an= A. an=B. (n∈N*),则该数列的通项公式为( )

an=C. D.a n= 9.已知数列{an}满足an+1=an﹣an﹣1(n≥2),a1=1,a2=3,记Sn=a1+a2+…+an,则下列结论正确的是( ) A. a100=﹣1,S100=5 C. a100=﹣3,S100=2 B. a100=﹣3,S100=5 D. a100=﹣1,S100=2 10.已知数列{an}中,a1=3,an+1=2an+1,则a3=( ) A. 3 优质范文

B. 7 C. 15 D. 18 .

11.已知数列{an},满足an+1=,若a1=,则a2014=( )

A. 12.已知数列?an?中,a1? A. 3()?2()

B. 2 C. ﹣1 D. 1 12n13n511n?1,an?1?an?(),,则an=( ) 6321n?11n?11n1nB. 3()?2() C. 2()?3() 2323D. 2()12n?11?3()n?1 3b1?0。13.已知数列?an?中,a1?1;数列?bn?中,当n?2时,an?( )

14.已知:数列{an}满足a1=16,an+1﹣an=2n,则 A. 8 B. 7 11求an,bn.(2an?1?bn?1),bn?(an?1?2bn?1),

33的最小值为( )

C. 6 D. 5 15.已知数列{an}中,a1=2,nan+1=(n+1)an+2,n∈N+,则a11=( ) A. 36 B. 38 C. 40 D. 42 16.已知数列{an}的前n项和为Sn,a1=1,当n≥2时,an+2Sn﹣1=n,则S2015的值为( ) A. 2015 二.填空题(共8小题) 17.已知无穷数列{an}前n项和

,则数列{an}的各项和为

B. 2013 C. 1008 D. 1007 18.若数列{an}中,a1=3,且an+1=an2(n∈N*),则数列的通项an= . 19.数列{an}满足a1=3,

=5(n∈N+),则an= .

20.已知数列{an}的前n项和Sn=n2﹣2n+2,则数列的通项an= . 21.已知数列{an}中,

22.已知数列{an}的通项公式an=

,则a16= .

,若它的前n项和为10,则项数n为 .

23.数列{an}满足an+1+(﹣1)nan=2n﹣1,则{an}的前60项和为 . 24.已知数列{an},{bn}满足a1=,an+bn=1,bn+1=

(n∈N*),则b2012= .

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三.解答题(共6小题)

25.设数列 {an}的前n项和为Sn,n∈N*.已知a1=1,a2=,a3=,且当a≥2时,4Sn+2+5Sn=8Sn+1+Sn﹣1. (1)求a4的值;(2)证明:{an+1﹣an}为等比数列; (3)求数列{an}的通项公式.

26.数列{an}满足a1=1,a2=2,an+2=2an+1﹣an+2. (Ⅰ)设bn=an+1﹣an,证明{bn}是等差数列; (Ⅱ)求{an}的通项公式.

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27.在数列{an}中,a1=1,an+1=(1+)an+.

(1)设bn=

,求数列{bn}的通项公式;

(2)求数列{an}的前n项和Sn.

28.(2015?琼海校级模拟)已知正项数列满足4Sn=(an+1)2. (1)求数列{an}的通项公式; (2)设bn=,求数列{bn}的前n项和Tn.

29.已知{an}是等差数列,公差为d,首项a1=3,前n项和为Sn.令和T20=330.数列{bn}满足bn=2(a﹣2)dn﹣2+2n﹣1,a∈R.

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{cn}的前20项