1 . 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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2024-03-21更新
|
1449次组卷
|
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江西省2024届高三下学期二轮复习阶段性检测数学试题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(已下线)数学(广东专用01,新题型结构)(已下线)压轴题05数列压轴题15题型汇总-1
2 . 已知数列
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce63cbbc51179a3cbfdd97fd6e7e0949.png)
(1)求
.
(2)求
的通项公式;
(3)设
的前
项和为
,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce63cbbc51179a3cbfdd97fd6e7e0949.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3641c1abb4b89e8030ab66a0418ca670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b0e085e70ec2c52608cecc2d29405f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的前
项和为
,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
________ ;若数列
的前
项和为
,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce818408925519703a4cf429e3ffbe7.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f3dd930d591a7debf35234d2763c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac8e1d60f036093acd1e8fb476226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d86563abbe61dc61282035deeaed84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce818408925519703a4cf429e3ffbe7.png)
您最近一年使用:0次
2023-05-11更新
|
959次组卷
|
4卷引用:吉林省实验中学2023-2024学年高二上学期期末考试数学试卷
吉林省实验中学2023-2024学年高二上学期期末考试数学试卷2023届山东省滨州市高三二模数学试题(已下线)专题11 数列前n项和的求法 微点7 并项法求和山东省烟台市中英文高级中学2023届高考模拟预测数学试题
名校
解题方法
4 . 已知数列
的首项是
,前
项和为
,且
,设
,若存在常数
,使不等式
恒成立,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/30d19b275977f479bb72675ca9faa284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b8d2b5198cec3059e3886060edf1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f8fd087de7eed4a69fde8e11d5e513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-01-25更新
|
3092次组卷
|
9卷引用:吉林省五校联考2021-2022学年高三上学期联合模拟考试数学(理科)试题
吉林省五校联考2021-2022学年高三上学期联合模拟考试数学(理科)试题吉林省四平市第一高级中学2021-2022学年高三上学期期末考试数学(理)试题湖北省部分学校2022届高三下学期5月适应性考试数学试题(已下线)考点9-2 基本不等式及其应用第四章 数列(单元测)(已下线)专题17 数列探索型、存在型问题的解法 微点3 数列探索型、存在型问题综合训练(已下线)专题04 数列(6)(已下线)数列与不等式专题03等比数列
5 . 设直线
:
与圆
:
交于不同的两点
,已知
,
,记数列
的前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c5e7bd6bac51402ffa04b4144ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c17b03d85cdffb23688f4ef31355d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a43765c31e6e60fac237d8b5885cc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189d4d5578a4b2e261f4316ae532dea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b3734df0b8f39f0f04b8c635d54248.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/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-03-04更新
|
575次组卷
|
3卷引用:吉林省长春吉大附中实验学校2021-2022学年高二上学期期末数学试题
6 . 在正项数列
中,
,
,
.
(1)求数列
与
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce1a2ca9bc6e81f7e942fca82c595fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37063ddf52a723f31c3aebdd429743d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39c3300bf689f857b22fdd3fbefbb6f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5767546f6a6ee5dd45bae2f441e677aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
7 . 设数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e6859180010cf0ae3cedaa58b88967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2010bd4895d6e85e59cabc1fd0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d1536d28d23c56c6f49d8d449fbcb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e6859180010cf0ae3cedaa58b88967.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-09-11更新
|
3005次组卷
|
3卷引用:吉林省梅河口市第五中学2019-2020学年高二9月月考数学(理)试题
名校
8 . 在等比数列
中,
.
(1)求
的通项公式;
(2)设
,数列
的前
项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76eedb8b626a77f8c26d2995bb37067c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea025149c457a3d5c6e508c82f7907f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/94351ce858fa3f3a09cfadc2d23d7253.png)
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