一、非标准
1.若数列{an}的首项a1=1,且an=an-1+2(n≥2),则a7等于( )
A.13 B.14 C.15 D.17
2.已知Sn为等差数列{an}的前n项和,a2+a8=6,则S9等于( )
A. B.27 C.54 D.108
3.在等差数列{an}中,a2=3,a3+a4=9,则a1a6的值为( )
A.14 B.18 C.21 D.27
4.在等差数列{an}中,a5+a6+a7=15,那么a3+a4+…+a9等于( )
A.21 B.30 C.35 D.40
5.(2014天津河西口模拟)设等差数列{an}的前n项和为Sn,若a11-a8=3,S11-S8=3,则使an>0的最小正整数n的值是( )
A.8 B.9 C.10 D.11
6.(2014浙江名校联考)已知每项均大于零的数列{an}中,首项a1=1,且前n项和Sn满足Sn-Sn-1=2(nN+,且n≥2),则a81等于( )
A.638 B.639 C.640 D.641
7.若等差数列{an}满足a7+a8+a9>0,a7+a10<0,则当n= 时,{an}的前n项和最大.
8.若等差数列{an}前9项的和等于前4项的和,且ak+a4=0,则k= .
9.已知公差大于零的等差数列{an}的前n项和为Sn,且满足a3·a4=117,a2+a5=22.
(1)求数列{an}的通项公式;
(2)若数列{bn}满足bn=,是否存在非零实数c使得{bn}为等差数列?若存在,求出c的值;若不存在,请说明理由.
10.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.
11.(2014辽宁,文9)设等差数列{an}的公差为d.若数列{}为递减数列,则( )
A.d>0 B.d<0 C.a1d>0 D.a1d<0
12.已知等差数列{an}的前n项和为Sn,S4=40,Sn=210,Sn-4=130,则n等于( )
A.12 B.14 C.16 D.18
13.若数列{an}满足:a1=19,an+1=an-3(nN+),则数列{an}的前n项和数值最大时,n的值为( )
A.6 B.7 C.8 D.9
14.已知正项数列{an}满足:a1=1,a2=2,2(nN+,n≥2),则a7= .
15.已知数列{an}的各项均为正数,前n项和为Sn,且满足2Sn=+n-4(nN+).
(1)求证:数列{an}为等差数列;
(2)求数列{an}的通项公式.
16.设数列{an}的前n项和为Sn,a1=1,an=+2(n-1)(nN+).
(1)求证:数列{an}为等差数列,并求an与Sn;
(2)是否存在自然数n,使得S1++…+-(n-1)2=2015?若存在,求出n的值;若不存在,请说明理由.
