高三数学二轮复习 专题高效升级卷8 等差数列与等比数列课件 文 新人教A版 课件.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,专题高效升级卷,8,等差数列与等比数列,一、选择题（本大题共,12,小题，每小题,4,分，共,48,分）,1.,设数列,a,n,的前,n,项和,S,n,n,2,，则,a,8,的值为（,）,A.15B.16,C.49D.64,答案：,A,2.,在等差数列,a,n,中，,a,3,a,6,a,9,27,，,S,n,表示数列,a,n,的前,n,项和，则,S,11,等于（,）,A.18B.198,C.99D.297,答案：,C,3.,已知数列,a,n,为等比数列，,S,n,是它的前,n,项和,.,若,a,2,a,3,2,a,1,，且,a,4,与,2,a,7,的等差中项为,，则,S,5,（,）,A.35B.33,C.31D.29,答案：,C,4.,已知等比数列,a,n,的公比为正数，且,a,3,a,9,2,a,5,2,，,a,2,2,，则,a,1,等于（,）,A.1B.,C.,D.2,答案：,B,5.,已知,a,n,为等差数列，,a,1,a,3,a,5,105,，,a,2,a,4,a,6,99,，以,S,n,表示数列,a,n,的前,n,项和，则使得,S,n,取得最大值的,n,是（,）,A.21B.20,C.19D.18,答案：,B,6.,设,a,n,为递减等比数列，,a,1,a,2,11,，,a,1,a,2,10,，则,lg,a,1,lg,a,2,lg,a,3,lg,a,10,等于（,）,A.,35B.35,C.,55D.55,答案：,A,7.,等差数列,a,n,中，若,a,1,，,a,2,011,为方程,x,2,10,x,16,0,的两根，则,a,2,a,1,006,a,2,010,等于（,）,A.10B.15,C.20D.40,答案：,B,8.,等差数列,a,n,中，,2,（,a,1,a,4,a,7,）,3,（,a,9,a,11,）,24,，则其前,13,项和为（,）,A.13B.26,C.52D.104,答案：,B,9.,已知等比数列,a,n,的各项均为正数，公比,q,1,，设,P,（,log,0.5,a,5,log,0.5,a,7,），,Q,log,0.5,，,P,与,Q,的大小关系是（,）,A.,P,Q,B.,P,Q,C.,P,Q,D.,P,Q,答案：,D,10.,数列,a,n,是公差不为,0,的等差数列，且,a,1,，,a,3,，,a,7,为等比数列,b,n,的连续三项，则数列,b,n,的公比为（,）,B.4,C.2D.,答案：,C,11.,等差数列,a,n,的前,n,项和,S,n,，若,a,3,a,7,a,10,8,，,a,11,a,4,4,，则,S,13,等于（,）,A.152B.154,C.156D.158,答案：,C,12.,等差数列,a,n,中，,S,n,是其前,n,项和，,a,1,2 011,，,2,，则,S,2,011,的值为（,）,A.,2 010B.2 010,C.,2 011D.2 011,答案：,C,二、填空题（本大题共,4,小题，每小题,4,分，共,16,分）,13.,已知数列,a,n,的前,n,项和,S,n,n,2,n,1,，则数列,a,n,的通项,a,n,.,答案：,14.,若,a,1,，,a,n,1,，,n,1,，,2,，,3,，,，则,a,n,.,答案：,15.,在等差数列,a,n,中，,a,1,0,，,a,10,a,11,0,，若此数列的前,10,项和,S,10,36,，前,18,项和,S,18,12,，则数列,|,a,n,|,的前,18,项和,T,18,的值是,.,答案：,60,16.,若数列,x,n,满足,lg,x,n,1,1,lg,x,n,（,n,N,*,），且,x,1,x,2,x,3,x,100,100,，则,lg,（,x,101,x,102,x,103,x,200,）的值为,.,答案：,102,三、解答题（本大题共,4,小题，每小题,9,分，共,36,分）,17.,已知等比数列,a,n,的公比,q,1,，,4,是,a,1,和,a,4,的一个等比中项，,a,2,和,a,3,的等差中项为,6,，若数列,b,n,满足,b,n,log,2,a,n,(,n,N,*,）,.,（,1,）求数列,a,n,的通项公式,;,（,2,）求数列,a,n,b,n,的前,n,项和,S,n,.,解：（,1,）因为,4,是,a,1,和,a,4,的一个等比中项，,所以,a,1,a,4,（,4,）,2,32.,由题意可得,因为,q,1,，所以,a,3,a,2,.,解得,所以,q,2.,故数列,a,n,的通项公式,a,n,2,n,.,（,2,）由于,b,n,log,2,a,n,(,n,N,*,),，所以,a,n,b,n,n,2,n,.,S,n,12,22,2,32,3,（,n,1,）,2,n,2,n,，,2,S,n,12,2,22,3,（,n,1,）,2,n,n,2,，,得,S,n,12,2,2,2,3,2,n,n,2,n,1,n,2.,所以,S,n,2,2,n,2.,18.,已知数列,a,n,的前,n,项和为,S,n,，,a,1,1,，,nS,（,n,1,）,S,n,n,2,cn,（,c,R,，,n,1,，,2,，,3,，,），且,S,1,，,，,成等差数列,.,（,1,）求,c,的值,;,（,2,）求数列,a,n,的通项公式,.,解：（,1,）,nS,（,n,1,）,S,n,n,2,cn,（,n,1,，,2,，,3,，,），,（,n,1,，,2,，,3,，,）,.,S,1,，,，,成等差数列，,.,.,c,1.,（,2,）由（,1,）得,1,（,n,1,，,2,，,3,，,），,数列,是首项为,，公差为,1,的等差数列,.,（,n,1,）,1,n,.,S,n,n,2,.,当,n,2,时，,a,n,S,n,S,n,1,n,2,（,n,1,）,2,2,n,1,，,当,n,1,时，上式也成立，,a,n,2,n,1,（,n,N,*,）,.,19.,已知数列,a,n,的前,n,项和,S,n,和通项,a,n,满足,S,n,（,1,a,n,）,.,（,1,）求数列,a,n,的通项公式,;,（,2,）求证：,S,n,;,（,3,）设函数,f,（,x,）,log,x,，,b,n,f,（,a,1,）,f,（,a,2,）,f,（,a,n,），求,T,n,.,解：（,1,）当,n,2,时，,a,n,（,1,a,n,）,（,1,a,n,1,）,a,n,a,n,1,，,化简得,2,a,n,a,n,a,n,1,，即,.,由,S,1,a,1,（,1,a,1,）得,a,1,，,数列,a,n,是首项,a,1,，公比为,的等比数列,.,a,n,（,）,n,1,（,）,n,.,（,2,）证法一：由,S,n,（,1,a,n,）得,S,n,1,（,）,n,.,1,（,）,n,1,，,1,（,）,n,.,S,n,.,证法二：由（,1,）知,a,n,（,）,n,，,S,n,1,（,）,n,.,1,（,）,n,1,，,1,（,）,n,，即,S,n,.,（,3,）,f,（,x,）,log,x,，,b,n,log,a,1,log,a,2,log,a,n,log,（,a,1,a,2,a,n,）,log,（,）,1,2,n,1,2,n,.,2,（,），,T,n,2,（,1,）（,）,（,）,.,20.,已知数列,a,n,的前,n,项和为,S,n,且满足,a,1,，,a,n,2,S,n,S,0,（,n,2,）,.,（,1,）求,S,n,和,a,n,;,（,2,）求证：,S,1,2,S,2,2,S,3,2,S,n,2,.,（,1,）解：由已知有,S,1,a,1,，,2,，,n,2,时，,a,n,S,n,S,n,1,2,S,n,S,.,当,时，有,，解得,.,若,则,与,矛盾,.,.,2,，即数列,是以,2,为首项，公差为,2,的等差数列,.,2,（,n,1,）,2,2,n,，,S,n,（,n,1,）,.,当,n,1,时，,a,1,;,当,n,2,时，,a,n,2,S,n,S,，,a,n,（,2,）证明：当,n,1,时，,S,1,2,，成立,.,当,n,2,时，,S,1,2,S,2,2,S,3,2,S,n,2,（,1,）,1,（,1,1,）,，,综上有,S,1,2,S,2,2,S,3,2,S,n,2,.,