1 . 若数列
的前
项和为
,关于正整数
的方程
记为
,命题
:对于任意的
,存在等差数列
使得
有解;命题
:对于任意的
,存在等比数列
使得
有解;则下列说法中正确的是( )
![](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/159f08aed9d004e3194fb892d49c9f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
A.命题![]() ![]() | B.命题![]() ![]() |
C.命题![]() ![]() | D.命题![]() ![]() |
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2 . 已知
是公差![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a4658ab94306d39aedda17deed7216.png)
的等差数列,其前
项和为
,
是公比
为实数的等比数列,
,
.
(1)求
和
的通项公式;
(2)设
,计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a4658ab94306d39aedda17deed7216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68b7cce6f8165a164c90c33430e2b17.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5b6ecc4aa0233cd3fcc4668a6bb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5249095e0c2a28875a40a5d9c2c56bac.png)
您最近一年使用:0次
3 . 已知数列
是各项为正的等比数列,
,
,则其前10项和
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259b2e755105c0ee479eabf7265a76a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
您最近一年使用:0次
2023-12-21更新
|
567次组卷
|
4卷引用:上海市奉贤区2024届高三一模数学试题
上海市奉贤区2024届高三一模数学试题上海市通河中学2023-2024学年高二上学期期末考试数学试题(已下线)专题05 数列(四大类型题)15区新题速递(已下线)上海市奉贤区2024届高三一模数学试题变式题6-10
4 . 已知等比数列
的前
项和为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.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/f9fb7d8b3adfc48e9605033e73645195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
您最近一年使用:0次
5 . 数列
中,
是正整数,数列
的前
项和
.
(1)若
,且
,求
的值;
(2)若
,求证
是等比数列,并求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7b198811c758c7e2f4cc259736c650.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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9710612f9f57bc75ed1119b0400fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5746b5cf1422ccfce16eaa5f7c1d2f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
6 . 若数列
的通项公式
(n为正整数),
的前n项和是
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf87455f218ab68dde0c4aaf19a0881.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94a20614ac3a6bd7146e12fbbd4e8d4.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/3cf87455f218ab68dde0c4aaf19a0881.png)
您最近一年使用:0次
7 . 已知数列
是严格增的等比数列,
,
.
(1)求
的通项公式;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cabe8a74ff165189787a700857acf64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ff57a2cd32a8a6beaa8dc62dac0536.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6574b44a3f8e46d987efd602f98ada93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd194aa295f6e12660c10291c29f6e5.png)
您最近一年使用:0次
名校
解题方法
8 . 若数列
满足:对于任意正整数n都有
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a408adeac2f85a001166aca21e3019.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cbb2f2389d1e35885178741929b320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a408adeac2f85a001166aca21e3019.png)
您最近一年使用:0次
9 . 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,有下列3个命题:
①若对任意的正整数
均有
,则
为和谐数列;
②若等差数列
是和谐数列,则
一定存在最小值;
③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.
以上3个命题中真命题的个数有( )个
![](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若对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
以上3个命题中真命题的个数有( )个
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2023-04-13更新
|
1191次组卷
|
5卷引用:上海市奉贤区2023届高三二模数学试题
上海市奉贤区2023届高三二模数学试题(已下线)专题06 数列及其应用(已下线)第三章 重点专攻二 不等式的证明问题(核心考点集训)(已下线)专题05 数列在高中数学其他模块的应用(九大题型+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)辽宁省沈阳市东北育才学校高中部2023-2024学年高三第六次模拟考试暨假期质量测试数学试题
10 . 已知等比数列
的前项和为
,若
,则
的公比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.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/59cea61d7e8eeaa7c0ac12424e132f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
您最近一年使用:0次