高中数学数列测试题附答案与解析.doc

强力推荐人教版数学高中必修5习题第二章 数列1an是首项a11，公差为d3的等差数列，如果an2 005，则序号n等于( )A667B668C669D6702在各项都为正数的等比数列an中，首项a13，前三项和为21，则a3a4a5( )A33B72C84D1893如果a1，a2，a8为各项都大于零的等差数列，公差d0，则( ) Aa1a8a4a5Ba1a8a4a5Ca1a8a4a5Da1a8a4a54已知方程(x22xm)(x22xn)0的四个根组成一个首项为的等差数列，则mn等于( )A1BCD 5等比数列an中，a29，a5243，则an的前4项和为( ).A81 B120 C168 D1926若数列an是等差数列，首项a10，a2 003a2 0040，a2 003a2 0040，则使前n项和Sn0成立的最大自然数n是( )A4 005B4 006C4 007D4 008 7已知等差数列an的公差为2，若a1，a3，a4成等比数列, 则a2( )A4B6C8D 108设Sn是等差数列an的前n项和，若，则( )A1B1C2D9已知数列1，a1，a2，4成等差数列，1，b1，b2，b3，4成等比数列，则的值是( )ABC或D10在等差数列an中，an0，an1an10(n2)，若S2n138，则n( )A38B20C10D9二、填空题11设f(x)，利用课本中推导等差数列前n项和公式的方法，可求得f(5)f(4)f(0)f(5)f(6)的值为 .12已知等比数列an中，(1)若a3a4a58，则a2a3a4a5a6 (2)若a1a2324，a3a436，则a5a6 (3)若S42，S86，则a17a18a19a20 .13在和之间插入三个数，使这五个数成等比数列，则插入的三个数的乘积为 14在等差数列an中，3(a3a5)2(a7a10a13)24，则此数列前13项之和为 .15在等差数列an中，a53，a62，则a4a5a10 .16设平面内有n条直线(n3)，其中有且仅有两条直线互相平行，任意三条直线不过同一点若用f(n)表示这n条直线交点的个数，则f(4) ；当n4时，f(n) 三、解答题17(1)已知数列an的前n项和Sn3n22n，求证数列an成等差数列.(2)已知，成等差数列，求证，也成等差数列.18设an是公比为 q 的等比数列，且a1，a3，a2成等差数列(1)求q的值；(2)设bn是以2为首项，q为公差的等差数列，其前n项和为Sn，当n2时，比较Sn与bn的大小，并说明理由19数列an的前n项和记为Sn，已知a11，an1Sn(n1，2，3)求证：数列是等比数列20已知数列an是首项为a且公比不等于1的等比数列，Sn为其前n项和，a1，2a7，3a4成等差数列，求证：12S3，S6，S12S6成等比数列.第二章 数列参考答案一、选择题1C解析：由题设，代入通项公式ana1(n1)d，即2 00513(n1)，n6992C解析：本题考查等比数列的相关概念，及其有关计算能力设等比数列an的公比为q(q0)，由题意得a1a2a321，即a1(1qq2)21，又a13，1qq27解得q2或q3(不合题意，舍去)，a3a4a5a1q2(1qq2)3227843B解析：由a1a8a4a5，排除C又a1a8a1(a17d)a127a1d，a4a5(a13d)(a14d)a127a1d 12d2a1a84C解析：解法1：设a1，a2d，a32d，a43d，而方程x22xm0中两根之和为2，x22xn0中两根之和也为2，a1a2a3a416d4，d，a1，a4是一个方程的两个根，a1，a3是另一个方程的两个根，分别为m或n，mn，故选C解法2：设方程的四个根为x1，x2，x3，x4，且x1x2x3x42，x1x2m，x3x4n由等差数列的性质：若gspq，则agasapaq，若设x1为第一项，x2必为第四项，则x2，于是可得等差数列为，m，n，mn5B解析：a29，a5243，q327， q3，a1q9，a13， S41206B解析：解法1：由a2 003a2 0040，a2 003a2 0040，知a2 003和a2 004两项中有一正数一负数，又a10，则公差为负数，否则各项总为正数，故a2 003a2 004，即a2 0030，a2 0040.S4 0060，S4 007(a1a4 007)2a2 0040，故4 006为Sn0的最大自然数. 选B(第6题)解法2：由a10，a2 003a2 0040，a2 003a2 0040，同解法1的分析得a2 0030，a2 0040，S2 003为Sn中的最大值Sn是关于n的二次函数，如草图所示，2 003到对称轴的距离比2 004到对称轴的距离小，在对称轴的右侧根据已知条件及图象的对称性可得4 006在图象中右侧零点B的左侧，4 007，4 008都在其右侧，Sn0的最大自然数是4 0067B解析：an是等差数列，a3a14，a4a16，又由a1，a3，a4成等比数列，(a14)2a1(a16)，解得a18，a28268A解析：1，选A9A解析：设d和q分别为公差和公比，则413d且4(1)q4，d1，q22，10C解析：an为等差数列，an1an1，2an，又an0，an2，an为常数数列，而an，即2n119，n10二、填空题11解析：f(x)，f(1x)，f(x)f(1x)设Sf(5)f(4)f(0)f(5)f(6)，则Sf(6)f(5)f(0)f(4)f(5)，2Sf(6)f(5)f(5)f(4)f(5)f(6)6，Sf(5)f(4)f(0)f(5)f(6)312（1）32；（2）4；（3）32解析：（1）由a3a5，得a42，a2a3a4a5a632（2），a5a6(a1a2)q44（3），a17a18a19a20S4q163213216解析：本题考查等比数列的性质及计算，由插入三个数后成等比数列，因而中间数必与，同号，由等比中项的中间数为6，插入的三个数之积为62161426解析：a3a52a4，a7a132a10，6(a4a10)24，a4a104，S13261549解析：da6a55，a4a5a107(a52d)49165，(n1)(n2)解析：同一平面内两条直线若不平行则一定相交，故每增加一条直线一定与前面已有的每条直线都相交，f(k)f(k1)(k1)由f(3)2，f(4)f(3)3235，f(5)f(4)42349，f(n)f(n1)(n1)，相加得f(n)234(n1)(n1)(n2)三、解答题17分析：判定给定数列是否为等差数列关键看是否满足从第2项开始每项与其前一项差为常数证明：（1）n1时，a1S1321，当n2时，anSnSn13n22n3(n1)22(n1)6n5，n1时，亦满足，an6n5(nN*)首项a11，anan16n56(n1)56(常数)(nN*)，数列an成等差数列且a11，公差为6（2），成等差数列， 化简得2acb(ac) 2，也成等差数列18解：（1）由题设2a3a1a2，即2a1q2a1a1q，a10，2q2q10，q1或（2）若q1，则Sn2n当n2时，SnbnSn10，故Snbn若q，则Sn2n ()当n2时，SnbnSn1，故对于nN+，当2n9时，Snbn；当n10时，Snbn；当n11时，Snbn19证明：an1Sn1Sn，an1Sn，(n2)Snn(Sn1Sn)，整理得nSn12(n1) Sn，所以故是以2为公比的等比数列20证明：由a1，2a7，3a4成等差数列，得4a7a13a4，即4 a1q6a13a1q3， 变形得(4q31)(q31)0， q3或q31(舍) 由； 111q61； 得 12S3，S6，S12S6成等比数列清水混凝土的配合比设计中，要针对当地水泥、砂石、外掺料及外加剂等原材料影响混凝土质量的多种因素进行分析，确定主要控制因素，并从经济性和使用要求综合考虑，优选出符合生产条件的最优方案组合。obstacles, correcting misunderstandings, advocate good cadre style. 2, adhere to the scientific decision-making and democratic decision-making decision-making law. Correctly handle to ensure that government decrees and based on the actual creative work, giving full play to subjective initiative, put an end to implement the conference meeting, to document the implementation of documents etc. Improve the scientific and democratic decision-making mechanism, improve and implement the decision to solicit the views of experts, the public hearing system. Improve the important decision of risk assessment mechanism and legal review mechanism. 3, to promote team unity. Uphold and improve the system of annual party book talk heart to heart, mind and Party members, Party members to exchange each other not less than 2 times. The implementation of sound team democratic life system, consolidate and enhance the partys mass line educational practice will promote the achievement of the topic of democratic life, criticism and self-criticism normalization, a long-term. Adhere to the party on the basis of the principle of unity, enhance internal communication, strengthen internal supervision, self Sleep maintenance team collective image and authority. (three) to ensure the execution is not strong or disguised to resist government decrees issues. Individual Bureau leadership team members lack of learning political theory system, not from the objective reality, not with the partys interests above all the principles to deal with personal problems. In the specific work safety supervision in the execution is not strong, in the implementation of the decision to deploy the discount, make choices, engage in work, the implementation of the agreement, uncomfortable is not performed, open or disguised to resist, the lack of subject consciousness of the party organization, the lack of resist in society all kinds of bad habits and unwholesome tendencies of courage Gas and courage. Such as the liability insurance of safe production work, individual leaders that have someone arrested, and no funding, not in the global chess perspective to the countryside to carry out daily inspection, found none of my business acceptance of the resumption of production in an armchair, with a pen, indifferent. Corrective measures: (LED Leadership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, to strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, To establish and perfect the muddle along and other issues. Bureau staff conduct work regulations, standardize the behavior of personnel. 2, strengthen the responsibility system. One is the in-depth study and implement the Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of (Hunan Office issued 2013 No.第 9 页 共 9 页