数学新设计同步北师大版必修五课件：第一章数列22(一).ppt

课前预习,课堂互动,课堂反馈,2.2,等差数列的前,n,项和,(,一,),学习目标,1.,体会等差数列前,n,项和公式的推导过程,(,难点,),；,2.,熟练掌握等差数列的五个量,a,1,，,d,，,n,，,a,n,，,S,n,的关系,，,能够由其中的三个求另外两个,(,重点,).,预习教材,P15,17,，,完成下列问题：,知识点一等差数列的前,n,项和公式,已知量,首项、末项与项数,首项、公差与项数,选用公式,S,n,_,S,n,_,【预习评价】,(1)S,n,1,2,3,n,_.,(2),已知等差数列,a,n,的首项,a,1,1,，公差,d,2,，则前,n,项和,S,10,(,),A.,20 B.,40,C.,60 D.,80,知识点二等差数列前,n,项和性质,【预习评价】,(1),在等差数列,a,n,中，,已知,a,13,10,，则,S,25,(,),A.230 B.240,C.250 D.260,(2),在等差数列,a,n,中，已知,S,2,2,，,S,4,8,，则,S,6,_.,答案,(1)C,(2)18,题型一等差数列的基本运算,【训练,1,】在等差数列,a,n,中；,(1),已知,a,6,10,，,S,5,5,，求,a,8,和,S,10,；,(2),已知,a,3,a,15,40,，求,S,17,.,题型二由数列的前,n,项和求,a,n,【例,2,】已知数列,a,n,的前,n,项和,S,n,2n,2,n,2.,(1),求,a,n,的通项公式；,(2),判断,a,n,是否为等差数列？,【训练,2,】已知数列,a,n,的前,n,项和,S,n,2n,2,3n.,求,a,n,的通项公式,.,解因为,S,n,2n,2,3n,，,所以当,n,2,时,，,S,n,1,2(n,1),2,3(n,1),2n,2,7n,5,，,a,n,S,n,S,n,1,4n,5,，,又当,n,1,时，,a,1,S,1,1,，满足,a,n,4n,5,，,所以,a,n,4n,5.,方向,1,利用,S,2n,1,(2n,1)a,n,解题,方向,2,利用,S,奇,与,S,偶,的关系解题,【例,3,2,】一等差数列共有偶数项，且奇数项之和与偶数项之和分别为,24,和,30,，最后一项与第一项之差为,10.5,，求此数列的首项、公差及项数,.,【例,3,3,】在等差数列,a,n,中，,S,10,100,，,S,100,10,，求,S,110,.,方向,3,利用等差数列的和生成等差数列解题,课堂达标,1.,若等差数列,a,n,的前,5,项和,S,5,25,，且,a,2,3,，则,a,7,等于,(,),A.12B.13,C.14 D.15,答案,B,答案,D,3.,设,S,n,是等差数列,a,n,的前,n,项和，,a,1,2,，,a,5,3a,3,，则,S,9,等于,_.,答案,54,4.,若数列,a,n,的前,n,项和,S,n,n,2,10n(n,1,，,2,，,3,，,),，则,a,10,_.,解析,a,10,S,10,S,9,(10,2,10,2,),(9,2,10,9),9.,答案,9,5.,在等差数列,a,n,中，,a,6,10,，,S,5,5,，求,a,8,和,S,8,.,课堂小结,ms-mouseenter=showCenter ms-mouseleave=hideCenter,欢迎您,