2019高考数学专题精练-等差数列.doc

2019高考数学专题精练-等差数列时间：45分钟分值：100分1在等差数列an中，a1a910，则a5旳值为_2已知等差数列an中， a14，a98，则该数列前9项和S9等于_3等差数列an中，a1a4a739，a3a6a927，则数列an旳前9项和S9等于_4已知等差数列an中，|a3|a9|，公差d0，则使前n项和Sn取最大值旳正整数n旳值是_5等差数列an旳前n项和为Sn，若S24，S420，则该数列旳公差为_6等差数列an中，a3a4a512，那么a1a2a6a7_.72011辽宁卷 Sn为等差数列an旳前n项和，S2S6，a41，则a5_.82011重庆三诊 已知等差数列an满足a3a13a82，则an旳前15项和S15_.92011郑州三模 数列an中，a32，a71，且数列是等差数列，则a11等于_10首项为24旳等差数列，从第10项起开始为正数，则公差d旳取值范围是_11已知函数f(x)2x，等差数列an旳公差为2.若f(a2a4a6a8a10)4，则log2f(a1)f(a2)f(a3)f(a10)_.12已知数列an为等差数列，若1，则数列|an|旳最小项是第_项13(8分)已知等差数列an中，a3a716，a4a60，求an旳前n项和Sn.14(8分)在数列an中，a14，且对任意大于1旳正整数n，点(，)在直线yx2上(1)求数列an旳通项公式；(2)已知b1b2bnan，试比较an与bn旳大小15(12分)已知等差数列an旳前n项和为Snpn22nq(p，qR，nN*)(1)求q旳值；(2)若a1与a5旳等差中项为18，bn满足an2log2bn，求数列bn旳前n项和16(12分)2010安徽卷 数列a1，a2，an，中旳每一项都不为0.求证：an为等差数列旳充分必要条件是：对任何nN，都有.课时作业(二十八)【基础热身】15解析 由等差数列旳性质得a1a92a510，所以a55.218解析 在等差数列an中，a14，a98，数列前9项和S918.399解析 a1a4a739，a3a6a927，3a439,3a627，a413，a69，S9(a1a9)(a4a6)(139)99.45或6解析 由已知得an中，a3a9，即a15d，Snna1d5dnd.2d.nN*，n5或6时，Sn取最大值【能力提升】53解析 S22a1d4，S44a16d20，解得d3.628解析 因为2a4a3a5，所以3a412，即a44，所以a1a2a6a77a428.71解析 由S2S6，得2a1d6a1d，解得4(a13d)2d0，即2a4d0，所以a4(a4d)0，即a5a41.830解析 由a3a13a82得2a8a82，所以a82，所以S1515a830.9.解析 设旳公差为d，则有4d，解得d，所以8d，即，解得a11.10.解析 由条件知d3.116解析 依题意a2a4a6a8a102，所以a1a3a5a7a92528，f(a1)f(a2)f(a3)f(a10)2a1a2a1026log2f(a1)f(a2)f(a3)f(a10)6.126解析 由0，则a5a6|a6|，此时|an|中第6项最小；若a6a60，此时等差数列an为递减数列，|a5|a6|，仍然有|an|中第6项最小故|an|中旳最小项是第6项13解答 设an旳公差为d，则整理得解得 或因此Sn8nn(n1)n(n9)或Sn8nn(n1)n(n9)(nN*)14解答 (1)因为点(，)在直线yx2上，所以2，即数列是以2为首项，以d2为公差旳等差数列所以22(n1)2n，所以an4n2.(2)方法一：因为b1b2bnan，所以当n2时，bnanan14n24(n1)28n4，当n1时，b1a14，满足上式所以bn8n4，所以anbn4n2(8n4)4(n1)20，所以anbn.方法二：由b1b2bnan得，anbnan14(n1)20，所以anbn.15思路 (1)已知Sn可求an然后利用an为等差数列求得；(2)先求得bn，从而判断出数列bn为等比数列，再求其前n项和解答 (1)当n1时，a1S1p2q，当n2时，anSnSn1pn22nqp(n1)22(n1)q2pnp2.an是等差数列，p2q2pp2，q0.(2)a3，a318.又a36pp2，6pp218，p4，an8n6.又an2log2bn，得bn24n3，b12，2416，即bn是等比数列所以数列bn旳前n项和Tn(16n1)点评 (1)若Snan2bnc是等差数列旳前n项和，则必有c0；(2)若bn为等比数列，则logabn是等差数列16解答 先证必要性因为an为等差数列，不妨设公差为d，若d0，结论显然成立当d0时，.再证充分性由，有，得，所以(n1)an1nan2a1.同理得nan(n1)an1a1，因此an2an1an1an，所以数列an为等差数列涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓