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填空题 | 一般(0.65) | 2022·全国高三专题练习
解题方法
1 . 等差数列eqId2c1230a9ef5a4968be599681d676dd2b的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqIdbc82f5e351f94d6ea832c619b78ac446eqId18c78343c6634c8ba109b6e9b7f3d35d,则使eqIddb5481de79c946c0a760143297d5eade取得最大值的eqId5f904d1376ac4de7a7d6cfea92ff6981______
更新:2021/07/31组卷:0
2 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,对一切eqId532dc4d959024b79b546428f5856e5aa,点eqId07106eb7416443968348381830d12dec都在函数eqIdb9df3860a3dc49499138374c49f01abc的图像上.
(1)将数列eqId93e38ecd74a24cb59da79181b95bfd3a依次按1项、2项、3项、4项循环地分为eqIdf8ce4aff05534ba4b6a76932e7feca92eqId5ce94aab476c4603abbbe2fd4076d3f1eqId41be0c58f2fb46bdab04a8aa4cb8cfa3eqId8d9d396476b14b87bef13745f73551ceeqId947ea708e301457dab4f87b59576471beqIdfcdf87d4b9964369b4eeb66004ca3679eqIda74071330df04e03a8ef35601bc0a81eeqId3e525888c7714de2988de1af510916a7eqIda2564aef23644807a9e565d21625ce7c、…,分别计算各个括号内各数之和,设由这些和按原来括号的前后顺序构成新的数列为eqIdeeb4ca98872f4e6d91cea28f43fc0b63,求eqId0099a995574f42b287c4829c24564c0c的值;
(2)设eqId174d58136ce34b5089892e7bb0dd4004为数列eqIdf6db94b159c847cfa6d16771500a88ba的前eqId5f904d1376ac4de7a7d6cfea92ff6981项积,若不等式eqIdd50e3f1213d8418eb82625d63ff580e1对一切eqId532dc4d959024b79b546428f5856e5aa都成立,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
单选题 | 一般(0.65) | 2021·北京二十中高二期末
解题方法
3 . 无穷数列eqId93e38ecd74a24cb59da79181b95bfd3ak个不同的数组成,前n项和为eqIddb5481de79c946c0a760143297d5eade,若对eqId6155d5095e254297bfa6a0166b195ce2,则k的最大值是(   )
A.3B.4C.5D.6
多选题 | 较易(0.85) | 2021·湖北高二期中
4 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a是等比数列,公比为eqIda5d0fc594d4048549d5bbda484fbecc8,前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eade,下列判断正确的有(   )
A.eqId88ef23c03cc5404f9ddfcd092ce5ed85为等比数列B.eqIdcfe70cee123d4c638c1678e7d097ca70为等差数列
C.eqId62e888038e7a4983be27989b76b284ae为等比数列D.若eqId1151b5278e4945e59c91962216cf85e3,则eqId496c66f8d2e44dc9b1ab5dec200f47ad
填空题 | 困难(0.15) | 2021·上海高三其他模拟
解题方法
5 . 将横坐标与纵坐标均为整数的点称为格点.已知eqIdab3420c074bf42698f587abb97ca7e48,将约束条件eqIdf04f296f3954453a9eb205a55dea5467表示的平面区域内格点的个数记作eqIddb5481de79c946c0a760143297d5eade,若eqId713228aab8334189a2cf1d6e6b976d89,则eqId7eeedd285a57477aa59f3ee5843651b3___________.
解答题 | 较易(0.85) | 2021·江西高一期末
6 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIdc1e4d301eec54450bd5d8b768691ec82,且eqId3c83a99fc98c4727a0b90e61fc6d05ab,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63各项均为正数,其前eqId5f904d1376ac4de7a7d6cfea92ff6981项和eqIddb5481de79c946c0a760143297d5eade满足eqId5622b33410c74d058aaa72f6365cfd35.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63的通项公式;
(2)令eqIde332381b54744dc0becfc593c94e7dc8,数列eqId74ef5fe5183946caaee41d8974816a20的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,求证:eqId7636ed09d0b447899cdaaa11585be805.
解答题 | 较难(0.4) | 2021·北京高考真题
7 . 定义eqIdb351db1a38f047b0a607f3dc83bbf489数列eqId93e38ecd74a24cb59da79181b95bfd3a:对实数p,满足:①eqId8b0a2b86f8854485b8eba9bf908f919ceqIdcf20a3934efe4730a8f7236c6c9bdac3;②eqIdea3867ca77f54c00a3602ced691c69c6;③eqIdc6e055cef3294956a5bd3bff1faa7e90eqId95afddb01e7147b5bc928c282276a846
(1)对于前4项2,-2,0,1的数列,可以是eqId8a1390aa3d754ef184290306ffa757dc数列吗?说明理由;
(2)若eqId93e38ecd74a24cb59da79181b95bfd3aeqId750a77d0e9bd45f2a33fbb8fd24ef8ec数列,求eqIdd80748a60dc04eb5bc4556d4e5cad370的值;
(3)是否存在p,使得存在eqIdb351db1a38f047b0a607f3dc83bbf489数列eqId93e38ecd74a24cb59da79181b95bfd3a,对eqId203e6e2aefa445b3ba3631bf2dbbe9cf?若存在,求出所有这样的p;若不存在,说明理由.
8 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId5f904d1376ac4de7a7d6cfea92ff6981项和为eqIddb5481de79c946c0a760143297d5eadeeqIdc8837fb516804d6783135f6c80de90e2eqId34713e30254547e7af1246e2387a6f6d,若eqIdc4da2ca7bf724394b2a5287ee55d576b,则eqId8c4243d3a68d483db73d7f4203c7e940(   )
A.10B.11C.12D.13
解答题 | 较难(0.4) | 2021·上海高三三模
解题方法
9 . 对于数列eqId93e38ecd74a24cb59da79181b95bfd3a,若存在常数eqId7cb034aea34347d7be649a03d8a054ed对任意eqId532dc4d959024b79b546428f5856e5aa恒有eqIdd121222fcb244605a7bef01799b9f4fe,则称eqId93e38ecd74a24cb59da79181b95bfd3a是“eqIdb61d7d58b34343a1bc06806d0400a71f数列”.
(1)首项为eqId75691f28a5bb4c8287401017aa3a2d29,公差为d的等差数列是否是“eqIdb61d7d58b34343a1bc06806d0400a71f数列”?并说明理由;
(2)首项为eqId75691f28a5bb4c8287401017aa3a2d29,公比为q的等比数列是否是“eqIdb61d7d58b34343a1bc06806d0400a71f数列”?并说明理由;
(3)若数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdb61d7d58b34343a1bc06806d0400a71f数列,证明:eqId240ad01bda794fe2a4964cd28019ae33也是“eqIdb61d7d58b34343a1bc06806d0400a71f数列”,设eqId07fe24f0509d4b8dab8eaafef43c2676,判断数列eqId29487bd4c116494baa04356b87bc5c5f是否是“eqIdb61d7d58b34343a1bc06806d0400a71f数列”?并说明理由.
解答题 | 困难(0.15) | 2021·北京八十中高三其他模拟
10 . 对于无穷数列eqId93e38ecd74a24cb59da79181b95bfd3aeqIdeeb4ca98872f4e6d91cea28f43fc0b63eqId532dc4d959024b79b546428f5856e5aa,若eqId182edd226e3a42fe954e6bb27e58f320eqId6d3103e573784addbe2f5b7c5e5e7daa,则称数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是数列eqId93e38ecd74a24cb59da79181b95bfd3a的“收缩数列”,其中eqIde432cc137b41493fa9bc2680e9b8826ceqId4779db8b5c714d67a4103532c2fb5c79分别表示eqIdf68adb27918348698dbb285f2f17e034中的最大项和最小项.已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqId92478644b29a4a0e8470a8c89d31b49f项和为eqIddb5481de79c946c0a760143297d5eade,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是数列eqId93e38ecd74a24cb59da79181b95bfd3a的“收缩数列”.
(Ⅰ)写出数列eqIdea32a138a2114bf0b5bb88afa06a413a的“收缩数列”;
(Ⅱ)证明:数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的“收缩数列”仍是eqIdeeb4ca98872f4e6d91cea28f43fc0b63
(Ⅲ)若eqIde6e9592348c445149e4257d16da14c78,求所有满足该条件的数列eqId93e38ecd74a24cb59da79181b95bfd3a
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