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,高中数学课件,灿若寒星整理制作,数学必修,5,等差数列复习课,授课人:高一数学组古丽拜克热木,艾沙,基础知识回顾,一、,定义,:,二、,通项公式,:,三、,等差中项,:,想一想,四,、,数列前,n,项和,:,基础知识回顾,五、,前,n,项和公式,:,*,。,对于公式整理后为,是关于,n,的没有常数项的二次函数,即:,六、等差数列的判定方法,(,1,),a,n,+1,-,a,n,=,d,(,常数,),a,n,是等差数列,(定义法),(,2,),2,a,n,+1,=,a,n,+a,n,+2,a,n,是等差数列,(递推法),(,3,),a,n,=kn+b,(,k,、,b,为常数,),a,n,是等差数列,(通项法),(,4,),S,n,=An,2,+Bn,(,A,、,B,为常数,),a,n,是等差数列,(求和法),七、等差数列的性质,1,.d,0,,,an,是递增数列,;,d,0,,,an,是递减数列;,d,=0,,,an,是常数列,.,2.,若,m,+,n,=,p,+,q,则,m+n=2k,,,则,若数列,a,n,是公差为,d,的等差数列,:,3.,a,n,是有穷等差数列,则与首末两项等距离的两项之和都相等,且等于首末两项之和,.,即,a,1,+a,n,=a,2,+a,n-1,=a,i,+a,n-,(,i-1,),=,4.,数列,ka,n,+b,(,k,、,b,是常数,),是公差为,kd,的等差数列,5.,下标成等差数列且公差为,m,的项,a,k,a,k+m,a,k+2m,组成公差为,md,的等差数列,6.,若,b,n,成等差数列,则,a,n,+b,n,,,ka,n,+b,n,(,k,为非零常数,),也是等差数列,7.,S,n,S,2n,-S,n,S,3n,-S,2n,也成等差数列,例,3.,已知数列,a,n,的前,n,项和为,S,n,=3,n,2,2,n,,求证数列,a,n,成,等差数列,并求其首项、公差、,通项公式,.,跟踪练习,1,:已知等差数列,a,n,中,,a,7,+,a,9,=16,a,4,=1,则,a,12,=(),2:,在等差数列,a,n,中,,S,15,=90,则,a,8,等于(),15,A:3B:4C:6D:12,C,A,6,4,、已知等差数列,a,n,的前,n,项和为,S,n,若,S,5,=5,S,10,=20,,求,S,15,.,解:,S,5,,,S,10,-S,5,,,S,15,-S,10,成等差数列,2(S,10,-S,5,)=S,5,+S,15,-S,10,即,30=5+S,15,-20,S,15,=45,练一练,作业,1.,复习有关内容,再见,
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