等差数列与等比数列教学ppt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,*,要点,疑点,考点,课 前 热 身,能力,思维,方法,延伸,拓展,误 解 分 析,第,1,课时 等差数列与等比数列,要点疑点考点 第1课时 等差数列与等比数列,要点,疑点,考点,1.等差(比)数列的定义,如果一个数列从第二项起，每一项与它的前一项的差(比)等于同一个常数，这个数列叫做等差(比)数列.,2.通项公式,等差,a,n,=a,1,+(n-1)d,，,等比,a,n,=a,1,q,n-1,3.等差(比)中项,如果在,a,、,b,中间插入一个数,A,，使,a,、,A,、,b,成等差(比)数列，则,A,叫,a,、,b,的等差(比)中项,A,(a+b),/,2,或,A,ab,要点疑点考点1.等差(比)数列的定义 2.通项公式,4.重要性质：,a,m,+a,n,a,p,+a,q,(,等差数列),a,m,a,n,a,p,a,q,(,等比数列),m+n=p+q,(,m,、,n,、,p,、,qN*),特别地,m+n=2p,a,m,+a,n,2a,p,(,等差数列),a,m,a,n,a,2,p,(,等比数列),返回,4.重要性质：am+anap+aq(等差数列)am,课 前 热 身,1.观察数列：30，37，32，35，34，33，36，()，38的特点，在括号内适当的一个数是_.,2.若关于,x,的方程,x,2,-x+a=0,和,x,2,-x+b=0,(,a,bR,且,ab,),的四个根组成首项为1/4的等差数列，则,a+b,的值为(,),A.3/8 B.11/24 C.13/24 D.31/72,3.,等比数列,a,n,的各项都是正数，且,a,2,a,3,/2,a,1,成等差数列，则,a,4,+a,5,a,5,+a,6,的值是(,),A.B.C.D.,或,31,D,B,课 前 热 身1.观察数列：30，37，32，35，34，3,4.,等比数列,a,n,中，,a,4,+a,6,=3,，则,a,5,(,a,3,+2a,5,+a,7,),=,_,5.,在等差数列,a,n,中，若,a,4,+a,6,+a,8,+a,10,+a,12,=,120,则,2,a,10,-a,12,的值为(,),A.20 B.22 C.24 D.28,C,9,返回,4.等比数列an中，a4+a6=3，则a5(a3+2a5,能力,思维,方法,【解题回顾】本题是利用等差数列、等比数列的条件设未知数，充分分析题设条件中量与量的关系，从而确定运用哪些条件设未知数，哪些条件列方程是解这类问题的关键所在.,1.四个正数成等差数列，若顺次加上2，4，8，15后成等比数列，求原数列的四个数.,能力思维方法【解题回顾】本题是利用等差数列、等比数列的条,2.,a,n,是等差数列，且,a,1,-a,4,-a,8,-a,12,+a,15,=2,，求,a,3,+a,13,的值.,【解题回顾】本题若用通项公式将各项转化成,a,1,、,d,关系后再求，也是可行的，但运算量较大.,2.an是等差数列，且a1-a4-a8-a12+a15=,【解题回顾】本题将函数、不等式穿插到数列中考查，用到了数学中重要的思想方法.,3.已知点,A,n,(,n,a,n,),为函数,F,1,y=,x,2,+1,上的点，,B,n,(n,b,n,),为函数,F,2,y=x,上的点，其中,n,N+,，设,c,n,=a,n,-b,n,(,n,N,+,).,(1),求证：数列,c,n,既不是等差数列也不是等比数列；,(2)试比较,c,n,与,c,n+1,的大小.,返回,【解题回顾】本题将函数、不等式穿插到数列中考查，用到了数学中,【解题回顾】本题对,sin,2,a,2,降次非常关键，不宜盲目积化和差,4.若,a,1,，,a,2,，,a,3,成等差数列，公差为,d,；,sin,a,1,，,sin,a,2,，,sin,a,3,成等比数列，公比为,q,，则公差,d=k,，,k,Z,延伸,拓展,【解题回顾】本题对sin2a2降次非常关键，不宜盲目积化和差,【解题回顾】依定义或通项公式，判定一个数列为等差或等比数列，这是数列中的基本问题之一.,5.,数列,a,n,与,b,n,的通项公式分别为,a,n,=2,n,，,b,n,=,3,n+,2,，它们的,公共项由小到大排成的数列是,c,n,.,写出,c,n,的前5项.,证明,c,n,是等比数列.,返回,【解题回顾】依定义或通项公式，判定一个数列为等差或等比数列，,误解分析,2.延伸拓展5中，证明一个数列是等比数列(或等差数列)，用有限项作比(差)得出常数是典型错误，应用,a,n+1,与,a,n,关系.,1.在用性质,m+n=p+q,则,a,m,+a,n,=a,p,+a,q,时，如果看不清下标关系，常会出现错误.,返回,误解分析2.延伸拓展5中，证明一个数列是等比数列(或等差数列,Module 2 Me,my parents and my friends,Unit 1 I can speak English,Module 2 Me,my parents and m,Introduce yourself:,My name is.,Im a.,Im from.,Im years old.,My favourite sport is.,Introduce yourself:My name is,Sports,Sports,play basketball,play basketball,play football,play football,play tennis,play tennis,play tennis,table,play tennistable,play the piano,play the piano,ride a bike,ride a bike,ride a horse,ride a horse,sing,sing,swim,swim,Match,Check the answer,Match Check the answer,Look,read and do,Swim,Sing,Ride a horse,Ride a bike,Play tennis,Play table tennis,Play football,Play basketball,Look,read and do SwimSingRide,What can Lingling do?,She can,swim,play football,and play tennis.,What can Lingling do?She ca,Listen and read,Listen and read,What,can,Betty do?,She,can,play football,play basketball,and speak English.,What,cant,Betty do?,She,cant,speak Chinese.,What can Betty do?She can play,He,can,play football,play table tennis,ride a bike and speak English.,What,cant,Tony do?,What,can,Tony do?,He,cant,swim.,He,cant,speak Chinese.,He can play football,play tab,Listen and repeat,Betty,can,play the piano.,Tony,can,play table tennis.,My friend,cant,speak English.,Betty,cant,play basketball.,Listen and repeatBetty can pla,Make a dialogue,Example:,-A:,Can,Betty speak English?,-B:Yes,she,can.,-A:,Can,Tony swim?,-B:No,he,cant.,Make a dialogueExample:,Name:,Can,Cant,Play basketball,Play football,Play table tennis,Play tennis,Play the piano,Ride a bike,Ride a horse,Sing,Swim,Cook,-Can you cook?,-Yes,I,can.,/,No,I,cant,.,Name:CanCantPlay basketballPl,Summery,I can.I cant.,He/She can.He/she cant.,Some sports,Can you?Yes,I can.,No,I cant.,Can he/she?Yes,he/she can.,No,he/she cant.,Summery I can.,Workbook,Workbook,