1 . 已知长轴长、短轴长和焦距分别为、
和
的椭圆
,点
是椭圆
与其长轴的一个交点,点
是椭圆
与其短轴的一个交点,点
和
为其焦点,
.点
在椭圆
上,若
,则( )
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.椭圆![]() ![]() |
D.![]() ![]() |
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2 . 对于函数
,若实数
满足
,则称
为
的不动点.已知
,且
的不动点的集合为
.以
和
分别表示集合
中的最小元素和最大元素.
(1)若
,求
的元素个数及
;
(2)当
恰有一个元素时,
的取值集合记为
.
(i)求
;
(ii)若
,数列
满足
,
,集合
,
.求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc955d158efde0bdd62d14a60a65e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4687da5aca206a4974ecbac6901e40aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51777d3fca1ee8f588a6c39190dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698f45c9ed5bb04924f1037107e76988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dec63e6d30a41fcc8972397875bf46.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc825a1d8739d18c7f2fcc0d489d4f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69742762f22dbde311d3cf86ffb00a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556c5ed8c16b568bdf3c674e57131770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49377a64a56c87bb4fb916f9ae427c1e.png)
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名校
解题方法
3 . 数列
满足:
是等比数列,
,且
.
(1)求
;
(2)求集合
中所有元素的和;
(3)对数列
,若存在互不相等的正整数
,使得
也是数列
中的项,则称数列
是“和稳定数列”.试分别判断数列
是否是“和稳定数列”.若是,求出所有
的值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4b7a84d1c2089430f5adbf0f52731e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2788ae6bae8e954fb96b9a3393adc19.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55e03428497ac0ea2aa80fe5bdcd939.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb0582b0e415def42abf1d0a567dccb.png)
(3)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f04755f109e1dc24e89113809280ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932441c3185a1e55e2dfda8ba7f1e419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
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5卷引用:浙江省温州市2024届高三第二次适应性考试数学试题
浙江省温州市2024届高三第二次适应性考试数学试题(已下线)第一套 艺体生新高考全真模拟 (二模重组卷1)湖北省黄冈市文海大联考2024届高三下学期临门一卷(三模)数学试题黑龙江省双鸭山市第一中学2023-2024学年高二下学期4月月考数学试题(已下线)专题07 数列通项公式与数列求和--高二期末考点大串讲(人教B版2019选择性必修第三册)
4 . 对于数列
(
),定义
为
,
,…,
中最大值(
)(
),把数列
称为数列
的“M值数列”.如数列2,2,3,7,6的“M值数列”为2,2,3,7,7,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daaf480839c9a4708d434c6bdb4f846b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.若数列![]() ![]() |
B.若数列![]() ![]() |
C.满足![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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7卷引用:河南省五市2024届高三第一次联考数学试题
河南省五市2024届高三第一次联考数学试题(已下线)第七套 艺体生新高考全真模拟 (一模重组卷)陕西师范大学附属中学2023-2024学年高二下学期第一次月考数学试题(已下线)模块四专题3重组综合练(陕西)(8+3+3+5模式)(北师大版高二)广东省广州市第六中学2023-2024学年高二下学期期中考试数学试题陕西省汉中市西乡县第一中学2023-2024学年高二下学期期中考试数学试题黑龙江省哈尔滨市第六中学2023-2024学年高二下学期期中考试数学试卷
5 . 已知数列
的前
项和为
,若数列
满足:①数列
项数有限为
;②
;③
,则称数列
为“
阶可控摇摆数列”.
(1)若等比数列
为“10阶可控摇摆数列”,求
的通项公式;
(2)若等差数列
为“
阶可控摇摆数列”,且
,求数列
的通项公式;
(3)已知数列
为“
阶可控摇摆数列”,且存在
,使得
,探究:数列
能否为“
阶可控摇摆数列”,若能,请给出证明过程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4ed75729a7f7a2d5a3d9f7293c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1798fb0c31c65218cd20e07320a17d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdaa641d2e7e17904c61ff7245a5cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7364bbda64feeb4d448f9316d4c67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa22ba45c62adc96ffe508594edd6900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca8076f0553088afded57b48009d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae2ea9de54e074c145b8259f6c55e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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6卷引用:吉林省白山市2024届高三第二次模拟考试数学试题
吉林省白山市2024届高三第二次模拟考试数学试题江西省2024届高三下学期二轮复习阶段性检测数学试题(已下线)数学(广东专用01,新题型结构)吉林省通化市梅河口市第五中学2024届高三下学期二模数学试题(已下线)压轴题05数列压轴题15题型汇总-1山东省淄博市实验中学2023-2024学年高二下学期第一次月考(3月)数学试卷
6 . 若
成等比数列,则公比为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae8a1c746e338bf224504c5c757b4c2.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
7 . 已知
,且
,函数
.
(1)记
为数列
的前
项和.证明:当
时,
;
(2)若
,证明:
;
(3)若
有3个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff69be9f14b645d71fe4547677db36de.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48241aafc046ccde27f7d63ae3018161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c98250092857464fbe6cc0707b89ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5a00e9328fe28c7f1f81377e05b044.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950581caec90a28b5fa8f1e81bf21d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a75bcd70f6b1a6d02dbb92e964e1b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知集合
是公比为2的等比数列且
构成等比数列.
(1)求数列
的通项公式;
(2)设
是等差数列,将集合
的元素按由小到大的顺序排列构成的数列记为
.
①若
,数列
的前
项和为
,求使
成立的
的最大值;
②若
,数列
的前5项构成等比数列,且
,试写出所有满足条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0784cd34f64a4d35e5b5d1293d0bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543d98f8ca582058c814c1fe20e1e87e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80701237101561e4ec3d0ab23199bc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220e4624092eced325989465266ac2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2853db0b85e810be7d37f2643c132a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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5卷引用:黑龙江省双鸭山市第三十一中学等校2024届高三第二次模拟数学试题
解题方法
9 . 某校组织知识竞赛,已知甲同学答对第一题的概率为
,从第二题开始,若甲同学前一题答错,则此题答对的概率为
;若前一题答对,则此题答对的概率为
.记甲同学回答第
题时答错的概率为
,当
时,
恒成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9763337e402b59931bdd67be439843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f726d8d4a9f897734c5d2ecbf01a0433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:黑龙江省双鸭山市第三十一中学等校2024届高三第二次模拟数学试题
解题方法
10 . 甲、乙、丙三名高中生进行传球训练.第一次由甲将球传出,传给乙的概率是
,传给丙的概率是
;乙传给甲和丙的概率都是
;丙传给甲和乙的概率地都是
.如此不停地传下去且假定每次传球都能被接到,记开始传球的人为第一次触球者,第
次触球者是甲的概率记为
.
(1)求
;
(2)证明:
为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7f8c30a765d615a050930cca542f44.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46dbb6c2b73d0bde7a4fdb732be161c1.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d82a35fbb7db16ff4b3191fbfa79f23.png)
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