32.(2015·北京·文T16)已知等差数列{an}满足a1+a2=10,a4-a3=2. (1)求{an}的通项公式;
(2)设等比数列{bn}满足b2=a3,b3=a7.问:b6与数列{an}的第几项相等? 33.(2015·重庆·文T16)已知等差数列{an}满足a3=2,前3项和S3=. (1)求{an}的通项公式;
(2)设等比数列{bn}满足b1=a1,b4=a15,求{bn}的前n项和Tn. 34.(2015·福建·文T17)等差数列{an}中,a2=4,a4+a7=15. (1)求数列{an}的通项公式;
(2)设bn=2????-2+n,求b1+b2+b3+…+b10的值.
2
35.(2015·全国1·理T17)Sn为数列{an}的前n项和.已知an>0,????+2an=4Sn+3.
9
2
(1)求{an}的通项公式;
(2)设bn=????,求数列{bn}的前n项和.
????+1
36.(2015·安徽·文T18)已知数列{an}是递增的等比数列,且a1+a4=9,a2a3=8. (1)求数列{an}的通项公式;
??+1
(2)设Sn为数列{an}的前n项和,bn=????,求数列{bn}的前n项和Tn.
????+1
1
??
37.(2015·天津·理T18)已知数列{an}满足an+2=qan(q为实数,且q≠1),n∈N,a1=1,a2=2,且a2+a3,a3+a4,a4+a5成等差数列.
(1)求q的值和{an}的通项公式;
(2)设bn=??22??,n∈N,求数列{bn}的前n项和.
2??-1
*
*
????????
38.(2015·山东·文T19)已知数列{an}是首项为正数的等差数列,数列{(1)求数列{an}的通项公式;
(2)设bn=(an+1)·2????,求数列{bn}的前n项和Tn.
1
????·????+1
}的前n项和为2??+1. ??
39.(2015·浙江·文T17)已知数列{an}和{bn}满足a1=2,b1=1,an+1=2an(n∈N),b1+2b2+3b3+…+??bn=bn+1-1(n∈N). (1)求an与bn;
(2)记数列{anbn}的前n项和为Tn,求Tn.
40.(2015·天津·文T18)已知{an}是各项均为正数的等比数列,{bn}是等差数列,且a1=b1=1,b2+b3=2a3,a5-3b2=7. (1)求{an}和{bn}的通项公式;
9
*
111
*
(2)设cn=anbn,n∈N,求数列{cn}的前n项和.
41.(2015·湖北·文T19)设等差数列{an}的公差为d,前n项和为Sn,等比数列{bn}的公比为q,已知b1=a1,b2=2,q=d,S10=100.
(1)求数列{an},{bn}的通项公式;
(2)当d>1时,记cn=????,求数列{cn}的前n项和Tn.
??
*
??
42.(2014·全国2·理T17)已知数列{an}满足a1=1,an+1=3an+1. (1)证明:{????+}是等比数列,并求{an}的通项公式; (2)证明:??+??+…+??<2.
??12
43.(2014·福建·文T17)在等比数列{an}中,a2=3,a5=81. (1)求an;
(2)设bn=log3an,求数列{bn}的前n项和Sn. 44.(2014·湖南·文T16)已知数列{an}的前n项和 Sn=2,n∈N.
(1)求数列{an}的通项公式;
(2)设bn=2????+(-1)an,求数列{bn}的前2n项和.
n
1
21113
??2+??
*
45.(2014·北京·文T14)已知{an}是等差数列,满足a1=3,a4=12,数列{bn}满足b1=4,b4=20,且{bn-an}为等比数列.
(1)求数列{an}和{bn}的通项公式; (2)求数列{bn}的前n项和.
46.(2014·大纲全国·理T18)等差数列{an}的前n项和为Sn.已知a1=10,a2为整数,且Sn≤S4. (1)求{an}的通项公式; (2)设bn=
1
,求数列{bn}的前n????????+1
项和Tn.
47.(2014·山东·理T19)已知等差数列{an}的公差为2,前n项和为Sn,且S1,S2,S4成等比数列. (1)求数列{an}的通项公式;
(2)令bn=(-1)????,求数列{bn}的前n项和Tn.
????+1
48.(2014·全国1·文T17)已知{an}是递增的等差数列,a2,a4是方程x-5x+6=0的根. (1)求{an}的通项公式;
2
n-1
4??
10
(2)求数列{??
??
2??}的前n项和.
49.(2014·安徽·文T18)数列{an}满足a1=1,nan+1=(n+1)an+n(n+1),n∈N*
.
(1)证明:数列{??
??
??}是等差数列;
(2)设bn
n=3·√????,求数列{bn}的前n项和Sn.
50.(2014·山东·文T19)在等差数列{an}中,已知公差d=2,a2是a1与a4的等比中项. (1)求数列{an}的通项公式; (2)设bn=
an(n+1)
2,记Tn=-b1+bn
2-b3+b4-…+(-1)bn,求Tn.
51.(2014·大纲全国·文T17)数列{an}满足a1=1,a2=2,an+2=2an+1-an+2. (1)设bn=an+1-an,证明{bn}是等差数列; (2)求{an}的通项公式.
52.(2014·全国1·理T17)已知数列{an}的前n项和为Sn,a1=1,an≠0,anan+1=λSn-1,其中λ为常数. (1)证明:an+2-an=λ;
(2)是否存在λ,使得{an}为等差数列?并说明理由.
53.(2013·全国2·文T17)已知等差数列{an}的公差不为零,a1=25,且a1,a11,a13成等比数列. (1)求{an}的通项公式; (2)求a1+a4+a7+…+a3n-2.
54.(2013·全国1·文T17)已知等差数列{an}的前n项和Sn满足S3=0,S5=-5. (1)求{an}的通项公式; (2)求数列{1
??
2??-1??2??+1
}的前n
项和.
55.(2012·湖北·理T18文T20)已知等差数列{an}前三项的和为-3,前三项的积为8. (1)求等差数列{an}的通项公式;
(2)若a2,a3,a1成等比数列,求数列{|an|}的前n项和. 56.(2011·全国·文T17)已知等比数列{a1
n}中,a1=3,公比q=1
3. (1)Sn为{an}的前n项和,证明:S1-??n=
??
2; (2)设bn=log3a1+log3a2+…+log3an,求数列{bn}的通项公式.
57.(2011·全国·理T17)等比数列{an}的各项均为正数,且2a1+3a2=1,??2
3=9a2a6.
(1)求数列{an}的通项公式;
11
(2)设b1
n=log3a1+log3a2+…+log3an,求数列{????
}的前n项和.
58.(2010·全国·理T17)设数列{a2n-1
n}满足a1=2,an+1-an=3·2.
(1)求数列{an}的通项公式;
(2)令bn=nan,求数列{bn}的前n项和Sn.
59.(2010·全国·文T17)设等差数列{an}满足a3=5,a10=-9, (1)求数列{an}的通项公式;
(2)求数列{an}的前n项和Sn及使得Sn最大的序号n的值.
12