名校
解题方法
1 . 对于数列
,若存在常数
对任意
恒有
,则称
是“
数列”.
(1)首项为
,公差为d的等差数列是否是“
数列”?并说明理由;
(2)首项为
,公比为q的等比数列是否是“
数列”?并说明理由;
(3)若数列
是
数列,证明:
也是“
数列”,设
,判断数列
是否是“
数列”?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd2bc3cabf815b6b840c95ca1e43520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
(1)首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
(2)首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c5777e5ec1fc5bc8d342e4eca81dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce96ae469b2ae51727788d29a05340.png)
您最近一年使用:0次
2021-05-29更新
|
573次组卷
|
4卷引用:课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)上海市嘉定区2021届高三三模数学试题(已下线)考点突破14 数列-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)上海市七宝中学2022届高三高考冲刺模拟1数学试题
名校
2 . 已知正项等比数列
中,
,
,用
表示实数
的小数部分,如
,
,记
,则数列
的前15项的和
为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21365765f67cbe258f15ace7499706b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5eee11a27eefa72fa8f80c9999ae2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f344fd588492f8bcbb5f55b2946ea735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00002246104870bd185a9d444bf138b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48ee1f6186fbfe28a0376c9a77f6573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da56a7efe431e83cd95bc3584ce8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973d17cd50a4905164d29b8449fafd52.png)
您最近一年使用:0次
2020-03-04更新
|
748次组卷
|
5卷引用:考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)上海市位育中学2021届高三三模数学试题(已下线)专题3 等比数列基本量运算(提升版)2020届安徽省淮北市第一中学高三上学期第四次月考数学(理)试题人教A版(2019) 选修第三册 过关斩将 第六章 6.3 综合拔高练
2021·上海浦东新·三模
名校
3 . 已知
,一个项数为
的有穷实数列
称为“
数列”,若其满足下列三个条件:①
;②当
时,
;③当
时,
.
(1)若存在
使得数列
为“
数列”,求x的值;
(2)已知存在有穷等比数列为“
数列”,求实数
的取值范围;
(3)设
是各项均为正整数的
项数列,
,
,且当
时,以
为通项的数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9a28e5fa25a2bf8dfd3feb0a140628.png)
都是“
数列”,求数列
最大项的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d233d8550ba789bdcfee2779e52702f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5e1bf3867fece175916228a47ef3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0d456c3023818bc5faa218390d7468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ec591761ff654e0383b31dac3ba0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2ddc89b522ced92e0f363b6e03fb10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ec591761ff654e0383b31dac3ba0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52740637d74c295300a299caa418390.png)
(1)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a198158fccb62629b55239ed348d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5e1bf3867fece175916228a47ef3f3.png)
(2)已知存在有穷等比数列为“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5e1bf3867fece175916228a47ef3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4546b288340a9393260ed532171518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037292a981f4dbf945a653eab6e91ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dd3c3b45125d4b484e2894992610f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f8404d363b828ad41e53f00af2d572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dd57b49718a8775bace62175049379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8758751cb1376c8457718a2402ae8913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9a28e5fa25a2bf8dfd3feb0a140628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a1df2c517cb5f6341c198447c0a687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b85c8c6ddab319a4f5666de759abd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
您最近一年使用:0次
4 . 已知数列
,
满足:存在
,对于任意的
,使得
,则称数列
与
成“k级关联”.记
与
的前n项和分别为
,
.
(1)已知
,判断
与
是否成“4级关联”,并说明理由;
(2)若数列
与
成“2级关联”,其中
,且有
,
,求
的值;
(3)若数列
与
成“k级关联”且有
,求证:
为递增数列当且仅当
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0255ada26e95a41ef6dff56d182db1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dafd98e5b223908b13013c3cacc0386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49189fbe8c6dff3dd5e434821cb90d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305bb62f5c255d4d3496e3b32a978712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f0143703027c50e08d92dcda0f962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa9cc746124e96ab7c55e2b94700ed0.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb29b58a739bfb2fdd878b09ef3c5435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055066d27bced0e6ffb17162be44cbd4.png)
您最近一年使用:0次
2022-11-06更新
|
348次组卷
|
8卷引用:专题17 数列(模拟练)
(已下线)专题17 数列(模拟练)上海市光明中学2022届高三模拟(一)数学试题上海市七宝中学2022届高三下学期6月月考数学试题(已下线)第06讲 第六章 数列综合测试(测)-2023年高考数学一轮复习讲练测(新教材新高考)(已下线)第10讲 数学归纳法与数列综合应用 - 1(已下线)专题06数列必考题型分类训练-3(已下线)专题17 数列(练习)-22022届上海市普通高等学校招生全国统一考试数学模拟试题(一)
名校
5 . 已知有穷数列
的各项均不相等,将
的项从大到小重新排序后相应的项数构成新数列
,称
为
的“序数列”.例如,数列
、
、
满足
,则其“序数列”
为1、3、2,若两个不同数列的“序数列”相同,则称这两个数列互为“保序数列”.
(1)若数列
、
、
的“序数列”为2、3、1,求实数x的取值范围;
(2)若项数均为2021的数列
、
互为“保序数列”,其通项公式分别为
,
(t为常数),求实数t的取值范围;
(3)设
,其中p、q是实常数,且
,记数列
的前n项和为
,若当正整数
时,数列
的前k项与数列
的前k项(都按原来的顺序)总是互为“保序数列”,求p、q满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c75058db8f3bce88c1ffd4eadf5f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fb1673b00229f4a9ba85fcf1e61d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65dc741612591192478ea0d1691e1b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
(2)若项数均为2021的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96c823084e586b1fea9e400e842a6e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b088cbabf546dd45f6218ea8d54926.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78cf45b8ebde48fe0771d7ac53c7fa77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d40ed6365809e9b4fa38fcb8850e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
您最近一年使用:0次
2021-12-24更新
|
764次组卷
|
5卷引用:数学-2022年高考押题预测卷02(上海专用)
(已下线)数学-2022年高考押题预测卷02(上海专用)上海市金山区2022届高三上学期一模数学试题上海市虹口高级中学2023-2024学年高二上学期期末考试数学试题(已下线)压轴题05数列压轴题15题型汇总-1湖南省衡阳市第八中学2024届高三适应性考试数学试题
6 . 已知数集
具有性质
:对任意的
与
两数中至少有一个属于
.
(1)分别判断数集
与
是否具有性质![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
(2)证明:
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf37bb0ce613aa440869a7db3abc26d.png)
(3)当
时,若
,若数集
具有性质
,求数集
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69edbd87b8d3d77f6e2ad2a3b460323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a76fd7d70aaa306d18a76e238365cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30692e554e0aa2bcfabd25c2ca4b391a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8564068ee1f073615fab9694b210e1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acdcfc22edc7cbc41fb7145e9976d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eace02560e7f1490694276c29a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf37bb0ce613aa440869a7db3abc26d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da4f52abad1deccf4bd6e100b9d36fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4332a0bc93d1044dc972ce0fbf755ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
您最近一年使用:0次
2022-10-18更新
|
319次组卷
|
5卷引用:单元高难问题01集合中的新定义问题-【倍速学习法】(沪教版2020必修第一册)
(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(沪教版2020必修第一册)上海市七宝中学2015-2016学年高一上学期第一次月考数学试题上海市大同中学2022-2023学年高一上学期10月月考数学试题上海市复兴高级中学2022-2023学年高一上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2023-2024学年高一上学期10月月考数学试题
名校
7 . 若数列
满足:对于任意的
,总存在
且
,使
成立,则称数
列为“Z数列”.
(1)若
,判断数列
是否为“Z数列”,说明理由;
(2)证明等差数列
为“Z数列”的充要条件是“
的公差d等于首项
”;
(3)是否存在既是等比数列又是“Z数列”的数列
?若存在,求出所有可能的公比的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d60e9f844afc9e372d0112bb2279214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738d701bf35c715a18b1e917d188a115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814698e07a0447e71fc9cb91504fcc33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c5b67b7e8d7d71d6ca7875d4c2de6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)是否存在既是等比数列又是“Z数列”的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2021-06-03更新
|
512次组卷
|
5卷引用:课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)上海市格致中学2021届高三三模数学试题(已下线)2021年新高考北京数学高考真题变式题16-21题沪教版(2020) 选修第一册 同步跟踪练习 第4章 测试卷北京市第五十五中学2023届高三上学期10月月考数学试题
8 . 定义:若无穷数列
满足
是公比为q的等比数列,则称数列
为“
数列”.设数列
中,
,
.
(1)若
,且数列
为“
数列”,求数列
的通项公式:
(2)设数列
的前n项和为
,且
,请判断数列
是否为“
数列”,并说明理由;
(3)若数列
是“
数列”,是否存在正整数m,n,使得
?若存在,请求出所有满足条件的正整数m,n;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631307e8ff61b215f447f2527c36e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d83f7ab72975f7588724dcd7726cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1196be612370e6db1275c1f087d010dd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab7d59ce066c8f0b346719003f8e28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d83f7ab72975f7588724dcd7726cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ed4e99e27a105a3984f96e139ccedd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d83f7ab72975f7588724dcd7726cca.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad95b9397983d0d63d2d67ccf138339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740b2c2f16c129d11e56ef30d5f08bae.png)
您最近一年使用:0次
2021-03-27更新
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6卷引用:考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)上海市敬业中学2021届高三下学期3月月考数学试题(已下线)专题04 《数列》中的解答题压轴题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)上海市南汇中学2022届高三下学期3月月考数学试题上海市延安中学2023-2024学年高二上学期期中数学试题江苏省南京市第九中学2023-2024学年高三上学期10月学情检测数学试题
解题方法
9 . 若数列
对任意连续三项
,均有
,则称该数列为“跳跃数列”.
(1)判断下列两个数列是否是跳跃数列:
①等差数列:
;
②等比数列:
;
(2)若数列
满足对任何正整数
,均有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc47df306e4bc72632047fbe01619bf9.png)
.证明:数列
是跳跃数列的充分必要条件是
.
(3)跳跃数列
满足对任意正整数
均有
,求首项
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4993aaab02cbc3cbed15d025f4b4e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dc2d44dfdb07c42acfb6eb6eec1f69.png)
(1)判断下列两个数列是否是跳跃数列:
①等差数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc28deef24c776e671639e6cfc028fa.png)
②等比数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9819764e7f56202270fd85e6841c9.png)
(2)若数列
![](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/bc47df306e4bc72632047fbe01619bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff03fcfa701aa0f42e914bd82afaaeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
(3)跳跃数列
![](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/2ae8a1b864e3e6d37a0eb027e661d9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
名校
10 . 数列
的前
项和为
,
,且对任意的
都有
,则下列三个命题中,所有真命题的序号是( )
①存在实数
,使得
为等差数列;
②存在实数
,使得
为等比数列;
③若存在
使得
,则实数
唯一.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194463e3b011603ff59c0789bcb65c40.png)
①存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
②存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
③若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694b52596fdfcc391b23b3894ad85ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bdc46d9f8256161c18158c1f5dc386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.① | B.①② | C.①③ | D.①②③ |
您最近一年使用:0次
2021-05-07更新
|
499次组卷
|
5卷引用:课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)(已下线)课时25 数列新定义-2022年高考数学一轮复习小题多维练(上海专用)上海市浦东新区2021届高三二模数学试题(已下线)数学-2022年高考押题预测卷02(北京卷)河南省周口市太康县第一高级中学2022-2023学年高二上学期第一次月考数学(文科)试题