优选教育等比数列课件

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,*,5.3,等比数列,【复习目标】,1,.,理解等比数列的概念,.,2,.,掌握等比数列的通项公式与前,n,项和公式,.,3,.,掌握等比中项的概念和性质,.,4,.,掌握等比数列的性质,.,【知识回顾】,5.3 等比数列【复习目标】,优选教育等比数列课件,优选教育等比数列课件,【,例题精解,】,【例题精解】,【例,2,】在等比数列中,a,1,=,2,a,4,=,54,求,q,与,S,4,;,a,1,=,2,S,3,=,26,求,q,与,a,3,;,a,2,=,18,a,4,=,8,求,a,1,与,q.,【分析】直接由通项公式与前,n,项和公式即可求得,.,请读者自行求解,.,【例2】在等比数列中,【分析】直接由通项公式与前n项和公,【例,3,】,(1)4,与,16,的等比中项是,.,(2),两个数的等差中项是,10,等比中项是,6,则这两个数是,(,),A,.,2,18B,.,4,16C,.,4,9D,.,3,12,(3),设,a,n,是等比数列,若,a,2,=,3,a,4,=,6,则,a,6,的值是,(,),A,.,9B,.,12C,.,16D,.,36,(4),设,a,n,是等比数列,且,a,n,0,a,2,a,4,+,2,a,3,a,5,+a,4,a,6,=,25,则,a,3,+a,5,=,(,),A,.,5B,.,10C,.,15D,.,20,(5),设,a,n,是等比数列,且,a,1,+a,2,+a,3,=,4,a,4,+a,5,+a,6,=,12,则,a,7,+a,8,+a,9,=,(,),A,.,20B,.,36C,.,15D,.,18,(6),设,a,n,是等比数列,a,2,a,3,=,8,a,4,a,5,=,128,则,a,6,a,7,=,.,【例3】(1)4与16的等比中项是.,优选教育等比数列课件,【例,4,】在,2,和,54,中间插入两个实数,使这四个数成等比数列,求公比和这两个数,.,【例4】在2和54中间插入两个实数,使这四个数成等比数列,【例,5,】在等比数列中,q=,2,a,1,+a,3,+a,5,+a,7,=,85,求,a,1,+a,2,+,+a,8,(,即,S,8,),【分析】把前,8,项分成奇数项与偶数项,已知奇数项的和为,85,求出偶数项的和即可,.,【解】,a,2,+a,4,+a,6,+a,8,=a,1,q+a,3,q+a,5,q+a,7,q,=q,(,a,1,+a,3,+a,5,+a,7,),=,2,85,=,170,S,8,=,85,+,170,=,255,.,【点评】本题应用了等比数列的定义,即,a,n+,1,=a,n,q.,其实也可以由,a,1,+a,3,+a,5,+a,7,=,85,求得首项,a,1,再由前,n,项和公式求得,S,8,.,【例5】在等比数列中,q=2,a1+a3+a5+a7=85,【,同步训练一,】,【,答案,】,C,一、选择题,1,.,下面有四个结论,由第,1,项起乘以相同常数得到后一项,这样所得到的数列一定为等比数列,;,常数列,a,a,一定为等比数列,;,等比数列,a,n,中,若公比,q=,1,则此数列各项相等,;,等比数列中,各项与公比都不能为零,.,其中正确结论的个数是,(,),A,.,0B,.,1C,.,2D,.,3,【同步训练一】【答案】C一、选择题,【,答案,】,B,【答案】B,【,答案,】,C,3.,在等比数列,a,n,中，,q,=3,，,S,6,=728,，,a,6,=(,),A,.,406B,.,360C,.,486D,.,286,【答案】C3.在等比数列an中，q=3，S6=728，a,【,答案,】,A,4,.,9,a,b,243,是等比数列,则,a,b,的值分别为,(,),A,.,27,81B,.,81,27C,.-,27,81D,.,27,-,81,【答案】A4.9,a,b,243是等比数列,则a,b的值分别,【,答案,】,A,5,.b,2,=ac,是三个非零实数,a,b,c,成等比数列的,(,),A,.,充要条件,B,.,充分但不必要条件,C,.,必要但不充分条件,D,.,既不充分又不必要条件,【答案】A5.b2=ac是三个非零实数a,b,c成等比数列的,【,答案,】,A,【答案】A,【,答案,】,A,【答案】A,【,答案,】,B,【答案】B,【,答案,】,C,9,.,在等比数列,a,n,中,已知,a,1,=,1,q=,2,则第,5,项至第,10,项的和为,(,),A,.,63B,.,992C,.,1008D,.,1023,【答案】C9.在等比数列an中,已知a1=1,q=2,则,【,答案,】,B,【答案】B,优选教育等比数列课件,三、解答题,16,.,在等比数列,a,n,中,a,6,=,192,a,8,=,768,求,a,1,q,S,10,.,三、解答题,17,.,在等比数列,a,n,中,a,5,-a,1,=,15,a,4,-a,2,=,6,求,a,3,和,q.,17.在等比数列an中,a5-a1=15,a4-a2=6,18,.,有四个数,其中前三个数成等差数列,后三个数成等比数列,并且第一个数与第四个数的和是,16,第二个数与第三个数的和是,12,求这四个数,.,18.有四个数,其中前三个数成等差数列,后三个数成等比数列,【,同步训练二,】,一、选择题,【,答案,】,C,【同步训练二】【答案】C,【,答案,】,A,【答案】A,【,答案,】,A,【答案】A,【,答案,】,D,4,.,在等比数列,a,n,中,若,a,1,a,9,是方程,2,x,2,-,5,x+,2,=,0,的两根,则,a,4,a,6,=,(,),A,.,5B,.,C,.,2D,.,1,【答案】D4.在等比数列an中,若a1,a9是方程2x2,【,答案,】,C,【答案】C,【,答案,】,C,【答案】C,【,答案,】,D,【答案】D,【,答案,】,A,【答案】A,【,答案,】,C,【答案】C,【,答案,】,B,10,.,在各项均为正数的等比数列,a,n,中,若,a,5,a,6,=,9,则,log,3,a,1,+,log,3,a,2,+,+,log,3,a,10,=,(,),A,.,12B,.,10C,.,8D,.,2,+,log,3,5,【答案】B10.在各项均为正数的等比数列an中,若a5a,16,64,-1,10,5,二、填空题,11.,等比数列,a,n,中,a,1,=-2,a,3,=-,8,则,a,n,=,.,12,.,若等比数列,a,n,中,a,4,=,1,a,7,=,8,则,a,6,与,a,10,的等比中项是,.,13,.,若,a,n,是等比数列,a,2,+a,3,=,9,a,4,+a,5,=,24,则,a,6,+a,7,=,.,14,.,在等比数列,a,n,中,a,5,a,9,是方程,x,2,+,5,x+,1,=,0,的两根,则,a,7,的值等于,.,15,.,在等比数列,a,n,中,若,a,4,a,7,+a,5,a,6,=,20,则此数列前,10,项的积为,.,-2,n,或,(-2),n,1664-1105二、填空题-2n或(-2)n,三、解答题,16.,在等比数列,a,n,中，,a,1,=2,q,=3,，求,a,2,，,a,3,，,a,4,，,a,5,.,三、解答题,优选教育等比数列课件,18.,等比数列,a,n,中，,a,3,=8,a,6,=64,，求公比,q,与,S,n,.,18.等比数列an中，a3=8,a6=64，求公比q与,