2.2.3等差数列的前n项和 (3)

*,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,等差数列前,n,项和,引例：,某仓库堆放的一堆钢管，最上面一层有,4,根钢管，下面的每一层都比上一层,多,一根，最下面的一层有,9,根，怎样计算这堆钢管的总数呢？,由此，对于一般的等差数列：,a,1,a,2,a,3,a,n,s,n =,a,1,+,a,2,+,a,3,+,+,a,n,s,n =,a,n,+,a,n-1,+,a,n-2,+,+,a,1,+,+,+,+,+,=,=,=,=,=,设,a,1,+,a,n,=,m,2,s,n,m,m,m,m,=,+,+,+,+,=,n,m,=,n,(,a,1,+,a,n,),s,n =,n,(,a,1,+,a,n,),2,思考：,一般的,如何求等差数列,a,n,的前,n,项和,S,n,？,引例：,由此，对于一般的等差数列：,a,1,a,2,a,3,a,n,s,n =,a,1,+,a,2,+,a,3,+,+,a,n,s,n =,a,n,+,a,n-1,+,a,n-2,+,+,a,1,+,+,+,+,+,=,=,=,=,=,设,a,1,+,a,n,=,m,2,s,n,m,m,m,m,=,+,+,+,+,=,n,m,=,n,(,a,1,+,a,n,),s,n =,n,(,a,1,+,a,n,),2,倒序相加法,等差数列的前,n,项和公式：,记忆方法：,a,1,a,n,n,特点：该公式与梯形面积公式,（上底,+,下底）,高,2,相似,s,n =,n,(,a,1,+,a,n,),2,变 形,a,n,=,a,1,+,(,n,1,),d,s,n =,n,a,1,n,(,n-,1,),d,2,等差数列的前,n,项和公式：,公式一,：,公式二,：,等差数列,a,n,的前,n,项和公式：,公式一,公式二,例,1,在等差数列,a,n,中,(1),已知,a,1,=,3,，,a,50,=,101,，求,S,50,(2),已知,a,1,=,3,，,d,=,1/2,，求,S,10,练习：,P,44,/,2(1)(2),(3),已知,a,1,=,-13,d,=,2,a,n,=,7,求,S,n,例,2,在等差数列,a,n,中，,(2),已知,d,=,1/2,a,n,=3/2,S,n,=,-,15/2,求,a,1,及,n,(1),已知,a,n,=2,n=12,S,n,=90,求,d,a,1,练习：,P47/4(1)(2),例,3,在等差数列,a,n,中，已知,第,1,项到第,10,项的和为,310,，,第,11,项到第,20,项的和为,910,，,第,21,项到第,30,项的和,求：,1.,一种方法：,课堂小结,（,1,）,（,2,）,2.,两个公式：,“,倒序相加法,”,等差数列,a,n,前,n,项和,作业：,课本：,P44/5,、,6,