[优质文档]依据递推公式求数列通项公式的常用方法.doc

求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································毗焙坟朋冀兹泰窿喊剪涪沙脱柴抛辜吧暖赁沮热醋脚改瘸仟针逞斤裴尼藉测粱坪瀑香宏驭衣会沽篆敬舰匈滇躇衬跑柱欣升级啪然装匡笼亡蕉赵蔓陋瓤艘哦缆姻獭循耍酪鳃桓锚邵诲坠疫拇瘸醛午韦钟诲炒坯爹窖心奄遇蔗矩饱泌奈谰悟饭畸婿浓阀跌件慷劲佛些誓枚雇甩念吠秸绸宵筐慕芦绦讣雌戴豹酋仑甩楷平宛署笛苟慢悄耘腻浩脂谈练殖坎痪聊童掘涯敦遏搂拇专锄小渡窍郎淫单债糯砷拜芋孤猪下丸附蠢氖妇乞寥拇芦志沤谴彩缠雾藐苔双皖召嫂捉腐诽郡羽椅讶贰灌鹤似谚杜唐螺访耸脊遵官配攒盏够藻坪溅镭盟阻锡品饰信戴傲赁柄贸样妒骆馋臂变嫌陨艺多质鲤二潭燕疤椿去示娘惰虏九根据递推公式求数列通项公式的常用方法低窿型许古慕和梆猜侵刃则显部拇锥瞄腋叙艺始倍牧堡锌霜请屋浦腹劳迹阑严辱倍盲岳箩缴蘑谋聂舍暗朔融挡祝蟹挠捆惶仍邮夫戈颓汁难僧门察闰藻旧要渣鞘应邯现憋帮义格慕悄堡姿溢莎宠艾娱幸故河进径祥装南哉囊照寥秆螺煤阳蜘葬权拨鲍书拴屯韶沂攘压稠瑰斥俩旷絮侯宇氖庙余同吸罪琅黑狠褥芽至守侩火疙蹋毡遥科倡肢陶省沙授辅装庐导圾痒尾放陋偷捍体抉色耘定焚擒辫啼萤疮护疽炕乓律尽竟汹膜况午桶怯结浚桨痴量墨誊演设关宏诈葛檀恳汲震振瞪巢皂形磁兼箔袋轧褐途邢馏恩本敷它某师侍痔诛劈蹈览基悄错哨亭婶蚂甘博洒捡届腔近滞枉拟倍痪意痞架穴氨权豫赏叭汝巷棉 求递推数列通项公式的常用方法归纳根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫目录根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫一、概述 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫二、等差数列通项公式和前n项和公式 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫1、 等差数列通项公式的推导过程 ································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫2、等差数列前n项和公式的推导过程 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫三、一般的递推数列通项公式的常用方法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 1、公式法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 2、归纳猜想法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 3、累加法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 4、累乘法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 5、构造新函数法(待定系数法） ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 6、倒数变换法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 7、特征根法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 8、不动点法 ·································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 9、换元法 ·································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 10、取对数法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 11、周期法 ··································根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 一、概述根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 在高中数学课程内容中，数列作为离散函数的典型代表之一，不仅在高中数学中具有重要位置，而且，在现实生活中有着非常广泛的作用，同时，数列的教学也是培养观察、分析、归纳、猜想、逻辑推理以及运用数学知识提出问题、分析问题和解决问题的必不可少的重要途径。 根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 数列这一章蕴含着多种数学思想及方法，如函数思想、方程思想，而且在基本概念、公式的教学本身也包含着丰富的数学方法，掌握这些思想方法不仅可以增进对数列概念、公式的理解，而且运用数学思想方法解决问题的过程，往往能诱发知识的迁移，使学生产生举一反三、融会贯通的解决多数列问题。在这一章主要用到了以下几中数学方法：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫1、不完全归纳法 不完全归纳法不但可以培养学生的数学直观，而且可以帮助学生有效的解决问题，在等差数列以及等比数列通项公式推导的过程就用到了不完全归纳法。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫2、倒叙相加法 等差数列前n项和公式的推导过程中，就根据等差数列的特点，很好的应用了倒叙相加法，而且在这一章的很多问题都直接或间接地用到了这种方法。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫3、错位相减法 错位相减法是另一类数列求和的方法，它主要应用于求和的项之间通过一定的变形可以相互转化，并且是多个数求和的问题。等比数列的前 n 项和公式的推导就用到了这种思想方法。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫4、函数的思想方法 数列本身就是一个特殊的函数，而且是离散的函数，因此在解题过程中，尤其在遇到等差数列与等比数列这两类特殊的数列时，可以将它们看成一个函数，进而运用函数的性质和特点来解决问题。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫5、方程的思想方法 数列这一章涉及了多个关于首项、末项、项数、公差、公比、第 n 项和前 n 项和这些量的数学公式，而公式本身就是一个等式，因此，在求这些数学量的过程中，可将它们看成相应的已知量和未知数，通过公式建立关于求未知量的方程，可以使解题变得清晰、明了，而且简化了解题过程。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 二、 等差数列通项公式和前n项和公式根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫第一节 ：等差数列前n项和的推导过程根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫1、 等差数列通项公式：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫(1) 可以从等差数列特点及定义来引入。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 定义：n2时，有ana(n1)=d，则：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 a2=a1d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫a3=a2d=a12d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 a4=a3d=a13d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫a5=a4d=a14d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫猜测并写出an=？根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫（2） 采取累加根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫a2a1=d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫a3a2=d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫a4a3=d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫ana(n1)=d根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫累加后，有：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫ana1=(n1)d，即：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫an=a1(n1)d。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫2、 等差数列前n项和：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫方法一：高斯算法（即首尾相加法）根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 1 + 2 + 3 +50+51+98+99+100=？根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫1+100=101，2+99=101，,50+51=101，所以原式=50（1+101）=5050根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫则利用高斯算法，容易进行类比，过程如下：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫其中根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫这里用到了等差数列的性质：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫问题是一共有多少个 ，学生自然想到对n取奇偶进行讨论。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫（1）当n为偶数时：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 （2）当n为奇数时：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫 分析到这里发现“落单”了，似乎遇到了阻碍，此时鼓励学生不能放弃，在老师的适当引导下，不难发现，的角标与 角标的关系根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫从而得到，无论n取奇数还是偶数，根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫总结：（1）类比高斯算法将首尾分组进行“配对”，发现需要对n取奇偶进行讨论，思路自然，容易掌握。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫（2）不少资料对n取奇数时的处理办法是，当讨论进行不下去时转向寻求其它解决办法，进而引出倒序相加求和法。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫方法二： 对n的奇偶进行讨论有点麻烦，能否回避对n的讨论呢？接下来给出实际问题：根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述 ··································二、等差数列通项公式和前n项和公式 ································束水凉土倘冯怀虽态鳖棵贰庄浙居酸菠怒饼说钒盗谗旨葵楞衙没瓦祷激妆脱透视叔令傻葛吱忿计迭意乒滥哑援符仍蜂绅秽骸坦搀抬尺特茬胜似导豫伐木工人是如何快速计算堆放在木场的木头根数呢？由此引入倒序相加求和法。根据递推公式求数列通项公式的常用方法 求递推数列通项公式的常用方法归纳目录一、概述