一、非標(biāo)準(zhǔn)
1.若數(shù)列{an}的首項(xiàng)a1=1,且an=an-1+2(n≥2),則a7等于( )
A.13 B.14 C.15 D.17
2.已知Sn為等差數(shù)列{an}的前n項(xiàng)和,a2+a8=6,則S9等于( )
A. B.27 C.54 D.108
3.在等差數(shù)列{an}中,a2=3,a3+a4=9,則a1a6的值為( )
A.14 B.18 C.21 D.27
4.在等差數(shù)列{an}中,a5+a6+a7=15,那么a3+a4+…+a9等于( )
A.21 B.30 C.35 D.40
5.(2014天津河西口模擬)設(shè)等差數(shù)列{an}的前n項(xiàng)和為Sn,若a11-a8=3,S11-S8=3,則使an>0的最小正整數(shù)n的值是( )
A.8 B.9 C.10 D.11
6.(2014浙江名校聯(lián)考)已知每項(xiàng)均大于零的數(shù)列{an}中,首項(xiàng)a1=1,且前n項(xiàng)和Sn滿足Sn-Sn-1=2(nN+,且n≥2),則a81等于( )
A.638 B.639 C.640 D.641
7.若等差數(shù)列{an}滿足a7+a8+a9>0,a7+a10<0,則當(dāng)n= 時(shí),{an}的前n項(xiàng)和最大.
8.若等差數(shù)列{an}前9項(xiàng)的和等于前4項(xiàng)的和,且ak+a4=0,則k= .
9.已知公差大于零的等差數(shù)列{an}的前n項(xiàng)和為Sn,且滿足a3·a4=117,a2+a5=22.
(1)求數(shù)列{an}的通項(xiàng)公式;
(2)若數(shù)列{bn}滿足bn=,是否存在非零實(shí)數(shù)c使得{bn}為等差數(shù)列?若存在,求出c的值;若不存在,請(qǐng)說明理由.
10.已知數(shù)列{an}的前n項(xiàng)和為Sn,a1=1,an≠0,anan+1=λSn-1,其中λ為常數(shù).
(1)證明:an+2-an=λ;
(2)是否存在λ,使得{an}為等差數(shù)列?并說明理由.
11.(2014遼寧,文9)設(shè)等差數(shù)列{an}的公差為d.若數(shù)列{}為遞減數(shù)列,則( )
A.d>0 B.d<0 C.a1d>0 D.a1d<0
12.已知等差數(shù)列{an}的前n項(xiàng)和為Sn,S4=40,Sn=210,Sn-4=130,則n等于( )
A.12 B.14 C.16 D.18
13.若數(shù)列{an}滿足:a1=19,an+1=an-3(nN+),則數(shù)列{an}的前n項(xiàng)和數(shù)值最大時(shí),n的值為( )
A.6 B.7 C.8 D.9
14.已知正項(xiàng)數(shù)列{an}滿足:a1=1,a2=2,2(nN+,n≥2),則a7= .
15.已知數(shù)列{an}的各項(xiàng)均為正數(shù),前n項(xiàng)和為Sn,且滿足2Sn=+n-4(nN+).
(1)求證:數(shù)列{an}為等差數(shù)列;
(2)求數(shù)列{an}的通項(xiàng)公式.
