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2022年2018届高三数学二轮复习数列专题及其答案 .pdf

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1、2018 届高三第二轮复习数列第 1 讲等差、等比考点【高考感悟】从近三年高考看，高考命题热点考向可能为：考什么怎么考题型与难度1.等差(比)数列的基本运算主要考查等差、等比数列的基本量的求解题型：三种题型均可出现难度：基础题2.等差(比)数列的判定与证明主要考查等差、等比数列的定义证明题型：三种题型均可出现难度：基础题或中档题3.等差(比)数列的性质主要考查等差、等比数列的性质题型：选择题或填空题难度：基础题或中档题1必记公式(1)等差数列通项公式：ana1(n 1)d.(2)等差数列前n 项和公式：Snn（a1 an）2na1n（n1）d2.(3)等比数列通项公式：ana1qn1.(4

2、)等比数列前n 项和公式：Snna1（q1）a1（1qn）1qa1 anq1q（q1）.(5)等差中项公式：2anan1an1(n2)(6)等比中项公式：a2nan1an1(n2)(7)数列 an的前 n 项和与通项an之间的关系：anS1（n1）Sn Sn1（n2）.2重要性质(1)通项公式的推广：等差数列中，anam(n m)d；等比数列中，anamqnm.(2)增减性：等差数列中，若公差大于零，则数列为递增数列；若公差小于零，则数列为递减数列等比数列中，若a10 且 q1 或 a10 且 0q1，则数列为递增数列；若a10 且 0 q1 或 a10 且 q 1，则数列为递减数列3易错提醒

3、(1)忽视等比数列的条件：判断一个数列是等比数列时，忽视各项都不为零的条件(2)漏掉等比中项：正数a，b 的等比中项是 ab，容易漏掉ab.【真题体验】1(2015 新课标高考)已知 an 是公差为1 的等差数列，Sn为 an的前 n 项和若 S84S4，则 a10()A.172B.192C10D12 2(2015 新课标高考)已知等比数列an满足 a114，a3a54(a41)，则 a2()A2 B1 C.12D.183(2015 浙江高考)已知 an是等差数列，公差d 不为零若a2，a3，a7成等比数列，且2a1a21，则 a1_，d_4(2016 全国卷 1)已知na是公差为3

4、的等差数列，数列nb满足12111=3nnnnbba bbnb1，.（I）求na的通项公式；（II）求nb的前 n 项和.【考点突破】考点一、等差（比）的基本运算1(2015 湖南高考)设 Sn为等比数列 an的前 n项和，若 a11，且 3S1，2S2，S3成等差数列，则 an_2(2015 重庆高考)已知等差数列 an满足 a32，前 3 项和 S392.(1)求 an的通项公式；(2)设等比数列 bn满足 b1a1，b4a15，求 bn的前 n 项和 Tn.文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6

5、D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档

6、编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6

7、D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档

8、编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6

9、D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档

10、编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6

11、D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8考点二、等差（比）的证明与判断【典例 1】(2017 全国 1)记 Sn为等比数列na的前 n项和，已知S2=2，S3=-6.（1）求na的通项公式；（2）求 Sn，并判断Sn+1，Sn，Sn+2是否成等差数列。.【规律感悟】判断和证明数列是等差(比)数列的三种方法(1)定义法：对于n 1 的任意自然数，验证an1an或an1an为同一常数(2)通项公式法：若 ana1(n1)dam(nm)d 或 anknb(nN*)，则 an为等差数列；若 ana1qn1amqnm或 anpq

12、knb(nN*)，则 an为等比数列(3)中项公式法：若 2anan1an1(nN*，n2)，则 an为等差数列；若 a2nan1an1(nN*，n2)，且 an0，则 an为等比数列变式：(2014 全国大纲高考)数列 an 满足 a11，a22，an22an1an2.(1)设 bn an1an，证明 bn是等差数列；(2)求an的通项公式考点三、等差（比）数列的性质命题角度一与等差(比)数列的项有关的性质【典例 2】(1)(2015 新课标高考)已知等比数列an满足 a13，a1a3a521，则 a3a5a7()A21B42C63D84(2)(2015铜陵模拟)已知等差数列an 的前 n

13、项和为 Sn，且 S1012，则 a5a6()A.125B12 C6 D.65文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

14、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

15、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

16、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

17、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

18、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

19、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8命题角度二与等差(比)数列的和有关的性质【典例 3】(1)(2014 全国大纲高考)设等比数列 an的前 n 项和为 Sn.若 S23，S415，则 S6()A31 B32C63 D64(2)(2015 衡水中学二调)等差数列 an中，3(a3a5)2(a7a10a13)24，则

20、该数列前 13 项的和是()A13 B26 C52 D156 针对训练 1在等差数列 an中，若 a3a4a5a6a725，则 a2a8_2在等比数列 an中，a4a816，则 a4a5a7a8的值为 _3 若等比数列 an 的各项均为正数，且 a10a11a9a122e5，则 ln a1ln a2 ln a20_【巩固训练】一、选择题1(2015 新课标高考)设 Sn是等差数列 an的前 n 项和若 a1a3a53，则 S5()A5B7C9D11 2(2014 福建高考)等差数列 an 的前 n 项和为 Sn，若 a12，S312，则 a6等于()A8 B10 C12 D14 3(2

21、014 重庆高考)对任意等比数列 an，下列说法一定正确的是()Aa1，a3，a9成等比数列Ba2，a3，a6成等比数列Ca2，a4，a8成等比数列Da3，a6，a9成等比数列4(2014 天津高考)设an是首项为 a1，公差为 1 的等差数列，Sn为其前 n 项和若 S1，S2，S4成等比数列，则 a1()A2 B2 C.12D125(2015 辽宁大连模拟)数列an 满足 anan1anan1(nN*)，数列 bn 满足 bn1an，且 b1b2 b990，则 b4b6()A最大值为 99 B为定值 99 C最大值为 100 D最大值为 200 二、填空题文档编码:CK9P9J5O2J4

22、HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J

23、5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4

24、HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J

25、5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4

26、HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J

27、5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4

28、HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P86(2015 陕西高考)中位数为1 010 的一组数构成等差数列，其末项为2 015，则该数列的首项为_7(2015 安徽高考)已知数列 an是递增的等比数列，a1a49，a2a38，则数列 an 的前n 项和等于_8(2014 江西高考)在等差数列 an 中，a17，公差为 d，前 n 项和为 Sn，当且仅当n8 时 Sn取得最大值，则 d 的取值范围为_三、解答题9(文)(2015 兰州

29、模拟)在等比数列 an 中，已知a12，a4 16.(1)求数列 an的通项公式；(2)若 a3，a5分别为等差数列bn的第 3 项和第 5 项，试求数列bn的前 n 项和 Sn.10、(2014 湖北高考)已知等差数列an满足：a12，且 a1，a2，a5成等比数列(1)求数列 an的通项公式；(2)记 Sn为数列 an 的前 n 项和，是否存在正整数n，使得 Sn60n 800？若存在，求n 的最小值；若不存在，说明理由11(2015 江苏高考)设 a1，a2，a3，a4是各项为正数且公差为d(d0)的等差数列(1)证明：2a1，2a2，2a3，2a4依次构成等比数列；(2)是否存在a1，

30、d，使得 a1，a22，a33，a44依次构成等比数列？并说明理由第 2 讲数列求和（通项）及其综合应用【高考感悟】文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

31、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

32、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

33、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

34、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8

35、文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6

36、K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8从近三年高考看，高考命题热点考向可能为：考什么怎么考题型与难度1.数列的通项公式考查等差、等比数列的基本量的求解；考查 an与 Sn的关系，递推关系等题型：三种题型均可出现难度：基础题或中档题2.数列的前n项和考查等差、等比数列前n 项和公

37、式；考查用裂项相消法、错位相减法、分解组合法求和.题型：三种题型均可出现，更多为解答题难度：中档题3.数列的综合应用证明数列为等差或者等比；考查数列与不等式的综合.题型：解答题难度：中档题【真题体验】1(2015 北京高考)设an是等差数列，下列结论中正确的是()A若 a1a20，则 a2a30 B若 a1a30，则 a1a20 C若 0a1a2，则 a2a1a3D若 a10，则(a2a1)(a2a3)0 2(2015 武汉模拟)已知等差数列 an 的前 n 项和为 Sn，a55，S515，则数列 1anan1 的前100 项和为()A.100101B.99101C.99100D.101

38、1003(2015 福建高考)等差数列 an 中，a24，a4a715.(1)求数列 an 的通项公式；(2)设 bn2an2n，求 b1b2b3 b10的值【考点突破】考点一、数列的通项公式【规律感悟】求通项的常用方法文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z

39、5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK

40、9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z

41、5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK

42、9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z

43、5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK

44、9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8(1)归纳猜想法：已知数列的前几项，求数列的通项公式，可采用归纳猜想法(2)已知 Sn与 an的关系，利用anS1，n1，SnSn1，

45、n2求 an.(3)累加法：数列递推关系形如an1 an f(n)，其中数列 f(n)前 n 项和可求，这种类型的数列求通项公式时，常用累加法(叠加法)(4)累乘法：数列递推关系如an1g(n)an，其中数列 g(n)前 n 项积可求，此数列求通项公式一般采用累乘法(叠乘法)(5)构造法：递推关系形如an1 panq(p，q 为常数)可化为 an1qp1p anqp1(p1)的形式，利用anqp1是以 p 为公比的等比数列求解递推关系形如an1pananp(p 为非零常数)可化为1an11an1p的形式1(2015 新课标高考)设 Sn是数列 an的前 n 项和，且a1 1，an1SnSn1，

46、则 Sn_2(2015 铜陵模拟)数列 an满足13a1132a213nan3n1，n N*，则 an_3若数列 an 满足 a13，an15an133an7，则 a2 015的值为 _考点二、数列的前 n 项和【规律感悟】1.分组求和的常见方法(1)根据等差、等比数列分组(2)根据正号、负号分组(3)根据数列的周期性分组2裂项后相消的规律常用的拆项公式(其中 nN*)1n（n1）1n1n 1.1n（nk）1k1n1nk.1（2n 1）（2n1）12(12n112n1)3错位相减法的关注点(1)适用题型：等差数列 an乘以等比数列 bn对应项(anbn)型数列求和(2)步骤：求和时先乘以数列b

47、n 的公比把两个和的形式错位相减整理结果形式4倒序求和。命题角度一基本数列求和、分组求和【典例 1】(2015 湖北八校联考)等差数列 an 的前 n 项和为 Sn，数列 bn是等比数列，满足a13，b11，b2 S210，a52b2a3.(1)求数列 an和 bn的通项公式；(2)令 cn2Sn，n为奇数，bn，n为偶数，设数列 cn的前 n 项和为 Tn，求 T2n.文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V

48、9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O

49、2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V

50、9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O2J4 HX6K6D8X3Z5 ZM5V9R3J5P8文档编码:CK9P9J5O

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关键词：: 2022年2018届高三数学二轮复习数列专题及其答案 2022 2018 届高三数学二轮复习数列专题及其答案

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