1 . 1.已知数列
的前
项和为
,从下面①②中任取一个作为条件,证明另外一个成立:
①
的前
项的和为
;
②
,且满足点
在斜率为2的直线上.
注:若两种情况都选择并分别解答,则按第一个解答计分.
![](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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ef47b5e69ecdfff71962615b2e1b06.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd2974f22054e744baf11dc860fb78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cbc6949c3f802bae26fd0530fdb0a7.png)
注:若两种情况都选择并分别解答,则按第一个解答计分.
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|
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2卷引用:四川省宜宾市普通高中2022届高三上学期第一次诊断测试理科数学试题
名校
解题方法
2 . 已知数列
的前
和
记
其中
表示不超过
的最大整数,如![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa5bb490d89e17614eaa183dde372f0.png)
(1)求数列
的通项公式;
(2)设
求数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6293e8e880645ab6becc56bb45f81a.png)
(3)求数列
的
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/60e29de843c67e6ece16e98098ed7771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9854d8159dafc79837543cf220b20575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa5bb490d89e17614eaa183dde372f0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02989d1a8ec24796c34dc86cc5dfcf83.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/8d6293e8e880645ab6becc56bb45f81a.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821b8672d030c240ff230a0174aa7a3d.png)
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解题方法
3 . 已知数列{an}的前n项和
,等比数列{bn}满足a1=3b1,b2b4=a2.
(1)求数列{an}的通项公式;
(2)求数列{b2n-1}的前n项和Tn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447de5925f6b257005f613d257f4566f.png)
(1)求数列{an}的通项公式;
(2)求数列{b2n-1}的前n项和Tn.
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2021-11-19更新
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2卷引用:四川省绵阳市江油市太白中学2024届高三上学期12月月考数学(文)试题
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解题方法
4 . 正项数列
的前
和为
,
,且
.
(1)求数列
的通项公式;
(2)求数列
的前
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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d315d99c4f4a5000985a630a94594053.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d22c28e82a93e04a6dfff80448c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4卷引用:四川省内江市威远中学2021-2022学年高三上学期第三次月考数学(理)试题
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解题方法
5 . 数列
的前
项和为
,点
在函数
的图象上.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,若不等式
对任意正整数
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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b759eb2e0c5b0ff0cf719c5375daf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5cf37f3ebb45d2f2eb29962d4247b7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667467e32bbaf18ca017d449b7e22f09.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/b1f9913eed1abde354deac79427cbbf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9卷引用:2017届四川省乐山市高三第一次调查研究考试文数试卷
名校
解题方法
6 . 已知数列
的前
项和
,等比数列
满足:
,
(
).
(Ⅰ)求数列
通项公式;
(Ⅱ)若数列
满足
,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/12e82f82ea3a90feeaf8d603859fb670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aa9c841db107532e7804bf7a0e0151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2480870dd79c5a97f63fe75e8af1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
7 . 已知数列{an}的前n项和为Sn,
,数列{bn}是等差数列,且b1=a1,b6=a5.
(1)求数列{an}和{bn}的通项公式;
(2)若
,记数列{cn}的前n项和为Tn,证明:Tn<8.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
(1)求数列{an}和{bn}的通项公式;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
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8 . 已知数列
的前
项和为
,满足
,设
,则数列
的前2021项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da14545c3b4016fe1da93959d72e1e88.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/25bdaa1dcde76250fdfabd69b6be95b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0700dec354397bda0ea3fbf2d7bc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da14545c3b4016fe1da93959d72e1e88.png)
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|
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4卷引用:四川省资阳市乐至中学2022-2023学年高三下学期开学考试数学(理)试题
四川省资阳市乐至中学2022-2023学年高三下学期开学考试数学(理)试题云南省曲靖市第二中学2021届高三二模数学(理)试题云南省曲靖市第二中学2021届高三二模数学(文)试题(已下线)模块综合练01 数列-2022年高考数学(文)一轮复习小题多维练(全国通用)
名校
解题方法
9 . 已知等差数列
的前
项和为
,
,
,数列
的
项和为
.
(1)求数列
和
的通项公式;
(2)若数列
满足
,求数列
的前2021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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa45ba57a920ce722a0e17307601b92.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/1c7c362fc435ebef6f36fe784250dc3c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50cbcafd81df7a9794bb141ba16b8771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7beada0668454b2cd7713cc3a520f0f3.png)
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2021-04-29更新
|
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10卷引用:四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题
四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题安徽省江淮十校2021届高三下学期4月第三次质量检测文科数学试题安徽省江淮十校2021届高三下学期4月第三次质量检测理科数学试题辽宁省沈阳市第二中学2021届高三五模数学(押题卷)试题(已下线)押新高考第18题 数列-备战2021年高考数学临考题号押题(新高考专用)(已下线)押第17题 数列-备战2021年高考数学(文)临考题号押题(全国卷1)(已下线)专题7.10 数列大题(分组、并项求和)-2022届高三数学一轮复习精讲精练(已下线)专题3.3 数列的综合问题(常规型)-2021年高考数学解答题挑战满分专项训练(新高考地区专用)河北省石家庄2022届高三上学期10月联考数学试题(已下线)押新高考第18题 数列-备战2022年高考数学临考题号押题(新高考专用)
名校
解题方法
10 . 已知数列
的前
项和为
,点
在函数
的图象上.
(1)求数列
的通项公式;
(2)设
,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/2cf9462100c8f7caa3339a17b82caace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7fd0dc2d4d51b804f843e22c26dac3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89aec7fca1046b12cb0e2857c913bba.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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2021-04-29更新
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10卷引用:四川省成都市郫都区2019-2020学年高一下学期期末考试数学(理科)试题
四川省成都市郫都区2019-2020学年高一下学期期末考试数学(理科)试题2014-2015学年贵州省绥阳中学高一下学期第三次月考数学试卷浙江省宁波市诺丁汉大学附属中学2019-2020学年高一(实验班)下学期期中数学试题陕西省咸阳市永寿县中学2020-2021学年高二上学期第一次月考数学试题宁夏银川六盘山高级中学2021届高三二模数学(文)试题重庆市西南大学附属中学2020-2021学年高二下学期期末数学试题(已下线)押新高考第18题 数列-备战2021年高考数学临考题号押题(新高考专用)(已下线)押第17题 数列-备战2021年高考数学(文)临考题号押题(全国卷1)(已下线)专题3.3 数列的综合问题(常规型)-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)押新高考第18题 数列-备战2022年高考数学临考题号押题(新高考专用)