1 . 记
为等差数列
的前
项和,已知
,
.
(1)求
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/9651204c54475c2e8cda8d0a6eeba177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5032706dd285c22e149c675da465d9ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2卷引用:陕西省西安市第一中学2023-2024学年高三下学期高考考前模拟考试理科数学试题
2 . 已知
是公差不为零的等差数列,其中
,
,
成等比数列,且
,数列
的前n项和为
.
(1)求数列
的通项公式及其前n项和
;
(2)设
求数列
的前n项和
;
(3)设集合
,求集合M中所有元素的和.
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e7b23fd74e3cf89ac541cb7a5d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93de8578f08e75e3622242c86273d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afe3a5de1da4001745c7b39547ebb8e.png)
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35次组卷
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2卷引用:广东省佛山市南海区第一中学2023-2024学年高二下学期阶段三暨期末统考模拟检测数学试题
解题方法
3 . 已知数列
各项均为正数,且
,记其前
项和为
.
(1)若数列
为等差数列,
,求数列
的通项公式:
(2)若数列
为等比数列,
,求满足
时
的最小值.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dfe5b322577f02fd19caab8cf20170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31a059268c7801f786e93a76d65b68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bedfcdf5e750f5451e0e5183c0d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
4 . 已知等差数列
的前
项和为
,公差为
,且
单调递增,若
,则
的取值范围为( )
![](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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b83d73d014a0ca4aff4282228312f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知公差不为0的等差数列
,前n项和为
,且
,_____.
现有条件:
;
;
.请从这三个条件中任选一个补充在上面题干中,并解决下面问题.
(1)求数列
的通项公式;
(2)若
,求数列{bn}的前n项和
.
(注:如果选择多个条件分别解答,按第一个解答计分.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
现有条件:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbd39d2e3eeef71b04ec59f74b091e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf003ccc2fd8aa62b0d6a98d0666771a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a603fd1e721cae04e5c5c2014280edba.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(注:如果选择多个条件分别解答,按第一个解答计分.)
您最近一年使用:0次
6 .
表示不小于x的最小整数,例如
,
.已知等差数列
的前n项和为
,且
,
.记
,则数列
的前10项的和______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa5efc9350c3ad41f456d434564f82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c314bd3e07c88abd2931344a30d11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739718565082441c3e1a9b3e22e1735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760775a38ed18ab8f346346e25de2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51814852f7070293f0e7ddcf4a0691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2dbf1896e958f7b0b715be6ab1b799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
您最近一年使用:0次
名校
解题方法
7 . 已知正项等差数列
的公差为2,前
项和为
,且
成等比数列.
(1)求数列
的通项公式
;
(2)若
求数列
的前
项和.
![](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/b91c13eaedd3a65b08e71d33a7a7c7a2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f05b1997d02b7483b7ece61061faba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b17a9b9bb8bf6bb9865e37f204da5c5.png)
您最近一年使用:0次
8 . 已知数列
为等比数列,
为等差数列,且
,
,
.
(1)求
,
的通项公式;
(2)若
,数列
的前n项和
;
①求数列
的前n项和
;
②对任意的
,不等式
恒成立,求实数
的取值范围.
![](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/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81f0ceacc025999ece67fb1bc2d452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf76ee8248d9d3435f52fd0a9fa73cb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1604a0743ed62d833577fd9929c376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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9 . 已知等差数列
的公差
,数列
为正项等比数列,且
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71c6e56da5da4a3cc0b2da1cf9dbbe9.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
10 . 已知数列
,数列
是等差数列且满足
.
(1)求数列
和
的通项公式;
(2)若
,求数列
的前
项和
;
(3)设数列
的前
项和为
,若
且
,求集合A中所有元素的和S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e61eea630134461c03372d259534e9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885b63770eceb375d9dd8120fbafb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设数列
![](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/f7df75474555327d95404531e9c3d0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f9e1111fb51de47d7e80476656e1e2.png)
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