人教版高中数学必修5《等差数列》精品学案.doc

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1、人教版高中数学必修5等差数列精品学案等差数列(1)等差数列(第1课时)【学习目标】1.通过课前热身练习，加深等差数列的概念的记忆，初步掌握等差数列的通项公式与前n项和公式；2.通过自主看书，建立起有关等差数列的知识网络结构；3.通过课堂演练，能判断一个数列是否为等差数列，能熟练应用等差数列的通项公式及前n项和公式解决相关问题.【学习重点】1.等差数列的判定与证明；2.等差数列通项公式及前n项和公式的应用.【学习难点】等差数列通项公式及前n项和的熟练应用.【热身练习】完成下列题目，并将题目考查的知识填空.1.在等差数列中，则（ ） A.12 B.14 C.16 D.18 考查 2.数列满足（）,

2、 ,是的前项和，则= 考查 3.设为等差数列，公差d=-2，为其前n项和.若,则 考查 4. 设为等差数列，已知则考查 【知识梳理】看书36页至45页，完成下列填空.1.等差数列的有关概念(1)定义：如果一个数列从第 项起，每一项与它的前一项的差等于 ，那么这个数列就叫做等差数列，这个常数叫做等差数列的 ，通常用字母 表示，定义的表达式为 .(2)等差中项：若成等差数列，则称是的 ，且 . 2.等差数列的通项公式：如果数列的首项为，公差为，那么通项公式为 3.等差数列的前n项和 = 【应用体验】一、等差数列的判定与证明体验1-1：在数列中,设，证明：是等差数列.体验1-2：给出下列等式：；数列

3、的前n项和，则数列an为等差数列的充要条件是( )A B C D小结：(1)判断或证明一个数列为等差数列一般采用 ，即证 .(2)判断一个数列为等差数列还可采用哪些方法？二、等差数列的通项公式与前n项和公式综合应用体验2：设是一个公差为的等差数列，它的前10项和且.求数列的通项公式.练习：设等差数列的前n项和为，已知，则 .(简单写一下解题过程)小结：三、等差数列前n项和的最值体验3：设等差数列的前n项和为，已知，求当n取何值时，取得最小值，并求出的最小值.变式探究：在等差数列中，已知，其前n项和为且，求当 时，取得最大值. (简单写一下解题过程)小结：在等差数列中，解决有关最值问题的方法有：

4、【晒晒收获】通过本节课的复习你有什么收获？你认为有哪些要注意的问题？【巩固练习】1.在数列中，且对任意大于1的正整数，点()在直线上，则= .2. .3.已知数列，其通项公式为，则其前n项和取得最小值时n的值为（ ） A.4 B.5 C.6 D.7【课后作业】1.设是等差数列的前n项和，若，公差，则 .2.等差数列中， .3.已知数列中，,若为等差数列，则 .4. 在等差数列中，则此数列的前13项的和为 .5.已知递减的等差数列满足，则数列的前n项和取最大值时 .6.在数列中，其中为常数，则 .7.若每一项都是整数的等差数列的首项为41，从第8项开始为负值，则公差 .8.等差数列中，是它的前n

5、项之和，且，则：此数列的公差；一定小于；是各项中的最大的一项；一定是的最大值.其中正确的是 .9.在等差数列中,为数列的前项和，已知，为数列的前项和，求.10.(选作题)已知数列的前n项和（n为正整数）.令，求证数列是等差数列，并求数列的通项公式.【拓展提升】1.等差数列的前n项和为，则使成立的n的最大值为 .2. 设等差数列的前n项和为，已知，则 .结束语！祝大家学到有用的知识，提升自己的能力，实现自己的梦想，踏踏实实干好每一件事，为美好的明天而努力！16jd6li8bdvwpijnm,.6omv61.w9ib38smwdyborp3fwftwbnj59k5v7nusub8o8u4671jf

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