组卷网>知识点选题>分类与整合思想
显示答案
| 共计 172 道试题
解答题 | 一般(0.65) |
1 . 已知数列eqId2c1230a9ef5a4968be599681d676dd2b的各项均为正数,前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且eqId7e876fbd55164cb495c852c9b382ee7c
(1)求证:eqId2c1230a9ef5a4968be599681d676dd2b为等差数列;
(2)设eqId114e5b543e2644a49dde45d125c5a857,求数列eqIda0db2906046940e19de8782f94f34137的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqId92ed363a54bd4a8a93df9463bb3af1f5
更新:2021/07/25组卷:213
2 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的首项为eqId2f362741818347e9b2007006deeff9b4,前n顶和为eqIddb5481de79c946c0a760143297d5eade
(1)若eqId21aaacd91f9746ee9f72a4b4e8b23dd2,求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)在(1)的条件下,是否存在eqId2f362741818347e9b2007006deeff9b4,使得对任意eqIdce57d815b3ae4582a03225a8fe63dccb,恒有eqId86532d354aa746e18e8c18622efabc58(其中k是与正整数n无关的常数),若存在,求出xk的值,若不存在,说明理由;
(3)若eqId93e38ecd74a24cb59da79181b95bfd3a是无穷等比数列,且公比eqId43aa5723d7044fb2bb6d5d8f8a26adbb,计算eqIdd821b1ccef04444fb4c163d040c7ff13
解答题 | 较难(0.4) | 2021·江西高一期末
3 . 数列可以看作是定义在正整数集的特殊函数,具有函数的性质特征,有些周期性的数列和三角函数紧密相连.记数列2,eqId49b7b111d23b44a9990c2312dc3b7ed9eqIdbeffaaf8d5cd43cf8375210d69fce6be,2,eqId49b7b111d23b44a9990c2312dc3b7ed9eqIdbeffaaf8d5cd43cf8375210d69fce6be,2,eqId49b7b111d23b44a9990c2312dc3b7ed9,-1,…为eqId93e38ecd74a24cb59da79181b95bfd3a,三角形式可以表达为eqId1dec47132d404db4b09ab7849df1f292,其中eqId0c10827df4214807ac8d1bda56ba2323eqId8ccf61601cf049d8a2100ee27d5b2419eqId9154c0ebe70946b8a8e6f5f0c686ba6f.
(1)记数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eade,求eqId66323e1f327444beacb68797109eb651eqIdb4de3265b5d64840ad8080068acf2dadeqId3ef2bfbb3f084a2382617254cdc86569eqIddb5481de79c946c0a760143297d5eade
(2)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的三角形式通项公式.
单选题 | 一般(0.65) | 2021·浙江高三月考
解题方法
同步
4 . 数列eqId13eb2908e50945b5802917d3108bb405满足eqId0cb91bd47ce84074b1abfeb9a35fe4cbeqIdacbf8e4d47ab4b1b8db35c8fa1fc0748eqIde130ee18c3584dd5ace39167d6ea2d1beqId9b68a00b1f024453a48859fec6cac847eqId5a8603b2220a4e4e98d139df002c30e2,当T取最小值时,该数列的前2021项的和是(   )
A.673B.674C.1347D.1348
解答题 | 困难(0.15) | 2021·上海高三二模
5 . 若数列eqId93e38ecd74a24cb59da79181b95bfd3a满足“对任意正整数eqIdb6e15e51d29a47a7aff44f98b1aafaeeeqIdc7d58dd623df4bdab3285964173faf12eqIdd9d5387d48ae44a2825d8deb95a66b4d,都存在正整数eqId4d2187284c5d4de29906363f7d21f60f,使得eqId551f9ac191504f81924dccc0762699dd”,则称数列eqId93e38ecd74a24cb59da79181b95bfd3a具有“性质eqIdbedf755e0fdb4d078d6859360706b163”.
(1)判断各项均等于eqId70a27b6ddf6b478285353abb3b1f3741的常数列是否具有“性质eqIdbedf755e0fdb4d078d6859360706b163”,并说明理由;
(2)若公比为eqIdc052ddfbd4524f67a79e0e77c2e5656a的无穷等比数列eqId93e38ecd74a24cb59da79181b95bfd3a具有“性质eqIdbedf755e0fdb4d078d6859360706b163”,求首项eqId75691f28a5bb4c8287401017aa3a2d29的值;
(3)若首项eqIdef51378d6b3048fc94aece7f1b93e1af的无穷等差数列eqId93e38ecd74a24cb59da79181b95bfd3a具有“性质eqIdbedf755e0fdb4d078d6859360706b163”,求公差eqId0beafc0779aa41fdb343d52e98143a82的值.
填空题 | 较难(0.4) | 2021·江西新余市·高三二模(文)
解题方法
压轴
6 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIda3cfd8fe19ee4cd89c40b975709518b4eqId1aefce7d6aa14b4d84ee83b8c8e79293eqId032284ef281340a78dbf643944ff8cd4,则eqId96c2f7fa4f144916b12fdb7763c586ae_______
解答题 | 较难(0.4) | 2021·上海高三二模
解题方法
8 . 已知无穷数列eqId2c1230a9ef5a4968be599681d676dd2b与无穷数列eqIda0db2906046940e19de8782f94f34137满足下列条件:①eqId5a37a6c7997a4c699f81607b2f504985;② eqId06d0779220b5462795d019c60ff6c7db.记数列eqIda0db2906046940e19de8782f94f34137的前eqId92478644b29a4a0e8470a8c89d31b49f项积为eqId92ed363a54bd4a8a93df9463bb3af1f5 .
(1)若eqIdb49b386239dc494db376649701216e65,求eqIdfc64b55e7fcf492bb47ded57cd03d0da
(2)是否存在eqIde60769385da9401b8706c42193021813,使得eqId7bff8bebdbc04f339070472e300a5876成等差数列?若存在,请写出一组eqIde60769385da9401b8706c42193021813;若不存在,请说明理由;
(3)若eqId46d68f4e66cf4136891c86d837a74e34,求eqIddfe2c07113724d03bb8353d5ee5ccfaf的最大值.
解答题 | 困难(0.15) | 2021·北京高三一模
9 . 已知无穷数列{an},对于mN*,若{an}同时满足以下三个条件,则称数列{an}具有性质P(m).
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得anTn=1,2,…);
条件③:anan+1man2n=1,2,…).
(1)若an=5+4eqId125def3606544bc58ccdd097b4c3556aeqId25fc0611ff9244528539fbb942016ccen=1,2,…),且数列{an}具有性质Pm),直接写出m的值和一个T的值;
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质Pm),且各项均为正整数,求数列{an}的通项公式.
解答题 | 较难(0.4) | 2021·全国高二课时练习
10 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的公差不为零,eqId555752ac7fa04b649f8577c02c16b684,且eqId13adbbc96007409baaae40269fd69a96成等比数列,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和为eqIddb5481de79c946c0a760143297d5eade,满足eqId7c7c5c3702e4489285ad4f0d9529ccb0.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)若数列eqId74ef5fe5183946caaee41d8974816a20满足:eqId840524116f9448dfbfe727b4e3c00832,求使得eqId2dcf78adf5ad4595924e72c97895ca2c成立的所有n值.
3道题,平均难度一般 清空试题 进入组卷中心
收起