名校
解题方法
1 . 若数列
满足
,则称该数列为“切线-零点数列”,已知函数
有两个零点1、2,数列
为“切线-零点数列”,设数列
满足
,
,数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780019495df34d40fff9d8f31bbf3e74.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293f1e5b48c2aaa93c1c510717ccdb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabd9b4d188ce62ce2f4105b6e4c9f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8efc620b5da3fdfaba2afa8cce8c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ecf43b8f2afb5584cafc66e0c33dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102cd7cdef652e6d04cd47773de5711c.png)
![](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/780019495df34d40fff9d8f31bbf3e74.png)
您最近一年使用:0次
名校
解题方法
2 . 设
是首项为3且公比为
的等比数列,则满足不等式
的最小正整数
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96432d89142c73879bac0d2d989738b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-12-06更新
|
473次组卷
|
2卷引用:上海市黄浦区2024届高三上学期期中调研测试(一模)数学试题
3 . 已知等比数列
是严格增数列,其第3、4、5项的乘积为1000,并且这三项分别乘以4、3、2后,所得三个数依次成等差数列.
(1)求数列
的通项公式;
(2)若对任意的正整数n,数列
的前n项和
,向量
的模为
,求数列
的前n项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若对任意的正整数n,数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716d6be9fcea44d5327c3e84184cd59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47effb08024b185f391f1177e77609d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2b289b20ecde54bf91c3a0bd5869e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9297e289a9ef977009186083ec738ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
您最近一年使用:0次
2023-12-06更新
|
319次组卷
|
2卷引用:上海市黄浦区2024届高三上学期期中调研测试(一模)数学试题
4 . 设
是一个无穷数列
的前
项和,若一个数列满足对任意的正整数
,不等式
恒成立,则称数列
为和谐数列,判断下列2个命题的真假:( )
①若等差数列
是和谐数列,则
一定存在最小值;
②若
的首项小于零,则一定存在公比为负数的一个等比数列是和谐数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edefd533852c96d0d8047c859d4bc458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.①假命题,②真命题 | B.①假命题,②假命题 |
C.①真命题,②假命题 | D.①真命题,②真命题 |
您最近一年使用:0次
5 . 在平面直角坐标系
中,点列
满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4748dcde982d277e7c74bc4df31eb6f6.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba480dfe9c03f4d22597a80db187de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d5987886f023f3fd913d21309c7395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96a5581bc5da9c4214cd384a45dca09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4748dcde982d277e7c74bc4df31eb6f6.png)
您最近一年使用:0次
6 . 已知
为等比数列,
的前
项和为
,前
项积为
,则下列选项中正确的是( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若数列![]() ![]() |
D.若数列![]() ![]() |
您最近一年使用:0次
7 . 若数列
为首项为3,公比为2的等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf14ebc775db2414a5a960badca8960.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf14ebc775db2414a5a960badca8960.png)
您最近一年使用:0次
2023-09-12更新
|
1080次组卷
|
4卷引用:上海市大同中学2024届高三上学期开学考数学试题
上海市大同中学2024届高三上学期开学考数学试题甘肃省白银市白银区大成学校2023-2024学年高二上学期月考(一)数学试题(已下线)4.3等比数列(2)(已下线)专题4.3 等比数列(5个考点八大题型)(3)
8 . 在数列
中,
.在等差数列
中,前
项和为
,
,
.
(1)求数列
和
的通项公式;
(2)设数列
满足
,数列
的前
项和记为
,试判断是否存在正整数
,使得
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa960b83e70e40e60e53a6d4334c0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe5fa40132bde317eb91fa3a399da23.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb8be0cd38e3e7f24ee873621d22731.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5fb39455abdcb71e7d35357c8569f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-06-20更新
|
619次组卷
|
2卷引用:上海市格致中学2023-2024学年高二上学期期中数学试题
9 . 在数列
中,
,
,其中
为给定的正整数.
(1)若
为等比数列,
,求
;
(2)若
为等差数列,求数列的前
项和
,并判断是否存在正整数
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a694aedf4c34c4fffbb7678e9aa3eade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8a878728b5a8ab809b7a10cff9fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eae7f0e85155e7d0076438398d1f229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
(2)若
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6858b87af2a83a7698a276772f6e7bfb.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
10 . 设数列
的前n项的和为
,若对任意的
,都有
,则称数列
为“K数列”.关于命题:①存在等差数列
,使得它是“K数列”;②若
是首项为正数、公比为q的等比数列,则
是
为“K数列”的充要条件.下列判断正确的是( )
![](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/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2c86af4416911af577d14afa08740d.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5713f1ebb4fcdf254a1e2dec5bdfbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.①和②都为真命题 | B.①为真命题,②为假命题 |
C.①为假命题,②为真命题 | D.①和②都为假命题 |
您最近一年使用:0次
2023-04-13更新
|
1012次组卷
|
6卷引用:上海市黄浦区2023届高三二模数学试题
上海市黄浦区2023届高三二模数学试题(已下线)专题06 数列及其应用上海市嘉定区2022-2023学年高二下学期期末数学试题上海市行知中学2023-2024学年高二上学期12月月考数学试卷(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)上海市大同中学2023-2024学年高一下学期5月月考数学试题