1 . 已知数列
是首项为1的等差数列,数列
满足
,且
,
.
(1)证明数列
是等比数列并求
的通项公式;
(2)令
,求数列
的前
项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1857d02529cce9ad6d1f80dc5c0f3bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368dc84a523ce87b9962505c06a9bfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36676cd8165b9136b1127e73565dac0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)令
![](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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2022-03-09更新
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992次组卷
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3卷引用:吉林省长春外国语学校2021-2022学年高三下学期期初考试数学(理)试题
2 . 已知公差不为0的等差数列
满足
,且
成等比数列.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18556fda4a825861f1170cdeb059ff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
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2021-11-12更新
|
1479次组卷
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3卷引用:吉林省长春外国语学校2021-2022学年高三下学期期初考试数学(文)试题
名校
解题方法
3 . 已知数列
为等差数列,
是数列
的前
项和,且
,
,数列
满足:
,当
时,
.
(1)求数列
,
的通项公式;
(2)令
,证明:
.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da12d94796c46513c3bab925b9ce229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a30ee33d5c1ba27228fbdf66943823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49e096ceb5cb120ec942f50e14885ff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8cd9b028ba9e5d70712133350d1b55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1badffaa2cef604b6685e3387cb03bf7.png)
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2021-11-12更新
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422次组卷
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7卷引用:吉林省吉林市2020届高三第四次调研测试数学(理)试题
解题方法
4 . (1)叙述并证明余弦定理;
(2)在
中,内角
所对的边分别为
,证明:
.
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63471f592531e46277365ed319e2acc.png)
您最近一年使用:0次
名校
解题方法
5 . 已知数列
的前n项和为
,且
,
.
(1)证明:数列
是等比数列,并求数列
的通项公式;
(2)若数列
的前n项和为
,
,且
,
,是否存在正整数k,使得
且
?若存在,求出k的值;若不存在,请说明理由.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68cc6414ac77edb084a13b5ea9f2867f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af933982377238c8931570df5918c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99622e8a419c74a9d417451ee16b9745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9de120173566422c32546c783789fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40035c0235c6ab19e05dde77e7ca64d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5928fc74d6331edb7f2abc9b706bccc.png)
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2022-01-27更新
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182次组卷
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2卷引用:吉林省通化市梅河口市第五中学2021-2022学年高二上学期期末数学试题
6 . 已知数列{an}中,a1=1,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4af77475b912dcdcd55b5bf3c4397cf.png)
(1)证明:数列{an﹣2}为等比数列;
(2)求数列{an}的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4af77475b912dcdcd55b5bf3c4397cf.png)
(1)证明:数列{an﹣2}为等比数列;
(2)求数列{an}的通项公式.
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9-10高一下·辽宁·期末
7 . 以数列的任意相邻两项为点
,
的坐标,均在一次函数
的图象上,数列
满足
,且
.
(1)求证:数列
是等比数列;
(2)设数列
,
的前
项和分别为
,
,若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079433d8cf832cc8ee996f87a7494a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea2cc14840d5f9439791c845156f53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e46d392f0dde0f80b3d1a31f969715f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dcd9dce9e95d00fb3569390faac22e.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f8af04e1b8ecddc64e455743998bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280c4c233f4ec2311dd1efddeb649251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2021-10-05更新
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7卷引用:2010年长春市十一高中高一下学期期末考试数学卷
(已下线)2010年长春市十一高中高一下学期期末考试数学卷2014-2015学年吉林省长春东北师大附中高一下学期期末文科数学卷(已下线)2010年辽宁省长春市十一高中高一下学期期末学生素质考试数学试题(文)(已下线)专题六 等比数列的前 n项和-2020-2021学年高中数学专题题型精讲精练(2019人教B版选择性必修第三册)沪教版(2020) 选修第一册 单元训练 第4章 单元测试(已下线)第四章 数列单元总结(思维导图+知识记诵+能力培养)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)(已下线)专题2 函数与数列
10-11高二下·山西临汾·期中
名校
解题方法
8 . 若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353a0504082335c98b71653317beabbe.png)
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14卷引用:吉林省长春市东北师范大学附属中学2020-2021学年第一学期第一次阶段考试数学试题
吉林省长春市东北师范大学附属中学2020-2021学年第一学期第一次阶段考试数学试题(已下线)2010-2011年山西省临汾一中高二第二学期期中考试文科数学2014-2015学年安徽省皖中“四校联盟”高一下学期联考文科数学试卷上海市建平中学2019-2020学年高一上学期期中数学试题(已下线)上海市华东师范大学第二附属中学2018-2019学年高一上学期期中数学试题江苏省南京市人民中学2020-2021学年高一上学期第一次调研考试数学试题江苏省南京师大附中2020-2021学年高一上学期期中数学试题(已下线)3.2.1 基本不等式的证明(练习)-2020-2021学年上学期高一数学同步精品课堂(新教材苏教版必修第一册)(已下线)2.2 基本不等式(精讲)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第一册)(已下线)专题02 不等关系-2022年(新高考)数学高频考点+重点题型高中数学解题兵法 第七十一讲 比较法(已下线)3.2 基本不等式(已下线)2.1不等式的性质(第4课时)福建省莆田第一中学2022-2023学年高一上学期10月考试数学试题
名校
解题方法
9 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7350cd628909cc2c660a0206573f4799.png)
(1)记
,求出
的值,并证明数列
为等比数列;
(2)若数列
的前2n项和为
,求满足不等式
的n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7350cd628909cc2c660a0206573f4799.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4188680e5320653753ad0340439cb77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb8c686dd9094f36105dadfbc985977.png)
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2021-12-04更新
|
574次组卷
|
3卷引用:吉林省吉林市第一中学2021-2022学年高二6月月考数学试题(理科创新班)
10 . 已知
为等差数列
的前
项和,
,
.
(1)求
;
(2)记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57964a9b6a7c4a9bad33c4316407c24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df86c3739c68507ed95bd207b2e78c42.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051e50e9a3fb2a8c63e171eaed229b2d.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/c215db1d8f69757118ad405b78035628.png)
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2021-04-16更新
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7卷引用:吉林省松原市前郭尔罗斯蒙古族自治县第五中学2020-2021学年高三5月月考数学试题
吉林省松原市前郭尔罗斯蒙古族自治县第五中学2020-2021学年高三5月月考数学试题河北省唐山市2021届高三下学期第二次模拟数学试题(已下线)第七章 数列专练3—等差数列前n项和-2022届高三数学一轮复习(已下线)第2讲 数列通项与求和(讲·)-2022年高考数学二轮复习讲练测(新教材地区专用)安徽省六安市新安中学2021-2022学年高三上学期第五次月考数学(文)试题2023版 湘教版(2019) 选修第一册 过关斩将 第1章 1.2.3等差数列的前n项和(已下线)第四章 数列(A卷·知识通关练) (3)