1 . 已知数列
的前
项和
,
是等差数列,且
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)令
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/11557edf05904133b3ba17c1a9ef8257.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/6060006090ff45aba1644f08d7e802d0.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/b33ab944f5904b3daa2282a3161442d2.png?resizew=85)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/f9c73fb7117f4028b639750ea384408d.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/98493a126759466fb63dae2fa9b3ef48.png?resizew=84)
(Ⅰ)求数列
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/f9c73fb7117f4028b639750ea384408d.png?resizew=31)
(Ⅱ)令
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/58b87d5229ce4423a6474d930fefbb0a.png?resizew=99)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/8912a8f082d748acb96a553e0c705bb5.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/6060006090ff45aba1644f08d7e802d0.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/28a749a510314d77832105d13cf07d7e.png?resizew=17)
您最近一年使用:0次
2 . 已知数列
的前
项和
,
是等差数列,且
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)令
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/11557edf05904133b3ba17c1a9ef8257.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/6060006090ff45aba1644f08d7e802d0.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/b33ab944f5904b3daa2282a3161442d2.png?resizew=85)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/f9c73fb7117f4028b639750ea384408d.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/98493a126759466fb63dae2fa9b3ef48.png?resizew=84)
(Ⅰ)求数列
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/f9c73fb7117f4028b639750ea384408d.png?resizew=31)
(Ⅱ)令
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/58b87d5229ce4423a6474d930fefbb0a.png?resizew=99)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/8912a8f082d748acb96a553e0c705bb5.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/6060006090ff45aba1644f08d7e802d0.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2017/5/3/1678957257564160/1679291562139648/STEM/28a749a510314d77832105d13cf07d7e.png?resizew=17)
您最近一年使用:0次
3 . 已知数列
满足
.
(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/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a387162fd9fd9916724e4bbf36edfd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9975297561960b78f563a2ef4aaef8be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
4 . 设数列
满足
,
,
.
(Ⅰ)求
的通项公式及前
项和
;
(Ⅱ)已知
是等差数列,且满足
,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106d71d47fffa137648f8cf30309e384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
(Ⅰ)求
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968ef8f37cbc55d57380015e0229f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a85b7320e28af5a31ce6b7ef10f96ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次
名校
5 . 设数列
满足
,
,
.
(Ⅰ)求
的通项公式及前
项和
;
(Ⅱ)已知
是等差数列,且满足
,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106d71d47fffa137648f8cf30309e384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
(Ⅰ)求
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968ef8f37cbc55d57380015e0229f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a85b7320e28af5a31ce6b7ef10f96ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次
2017-03-07更新
|
412次组卷
|
4卷引用:辽宁省大连市2016-2017学年高二上学期期末考试数学(理)试题
名校
6 . 已知等差数列
满足:
,且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)记
为数列
的前
项和,是否存在正整数
,使得
?若存在,求
的最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)记
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629ebe5a62685ba4efbc30e7e0cae4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2017-03-06更新
|
2913次组卷
|
20卷引用:2016-2017学年河北馆陶县一中高二上期中数学试卷
2016-2017学年河北馆陶县一中高二上期中数学试卷2016-2017学年河南省平顶山市高二上学期期末调研考试数学(文)试卷山东省济南外国语学校、济南第一中学等四校2017-2018学年高二上学期期末考试数学(文)试题智能测评与辅导[理]-等差数列人教A版 成长计划 必修5 第二章数列 高考链接2019届青海省西宁市湟川中学高三上学期11月数学试题黑龙江省七台河市第一中学2019-2020学年高一下学期数学4月线上考试试题湖北省武汉市三校联合体2019-2020学年高一下学期期中数学试题(已下线)题型08 等差数列、等比数列综合问题-2020届秒杀高考数学题型之数列四川省成都市第七中学2020年普通高等学校招生统一热身考试理科数学试题四川省成都市第七中学2020年普通高等学校招生统一热身考试文科数学试题四川省成都市第七中学2020届高三高考(7.2)热身考试文科数学试题(已下线)河南省平顶山市2016-2017学年高二上学期期末调研考试文数试题北京市北京师范大学附属实验中学2020-2021学年高二下学期期中考试数学试题四川省成都市双流中学2021-2022学年高三上学期第一次阶段性检测数学(理)试题陕西省宝鸡市渭滨区2022届高三下学期二模理科数学试题陕西省宝鸡市渭滨区2022届高三下学期二模文科数学试题(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21 数列解答题(理科)-1(已下线)专题21 数列解答题(文科)-1
2011·河北唐山·一模
7 . 已知数列
满足:
,且
.
(1)求证:数列
为等差数列;
(2)求数列
的通项公式;
(3)求下表中前n行所有数的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887d4bfa6aa62a9489809efbca4340d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a54f3e64c4132a3d57da56d17c60fb5.png)
……………………………
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b133a67fbb2c527ba166f0dede952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d20bf0547d21d0d95e9126cbca2753.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576b8a96318251cedee755512e73e7c9.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求下表中前n行所有数的和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4350dddc7cca2eac5f2671c6ea8370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887d4bfa6aa62a9489809efbca4340d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a54f3e64c4132a3d57da56d17c60fb5.png)
……………………………
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee0b81d1a127dfdb7a1b705f87661bf.png)
您最近一年使用:0次
名校
8 . 设公差不为零的等差数列
的前
项和为
,且
成等比数列.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92128c6c226ce688bc160fb86854f2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192a47ab17ed5c588efc6d161889820c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b061d3478c4ca323959ab233e20fe3.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/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
2016-12-05更新
|
1148次组卷
|
6卷引用:2017届江苏南通中学高三上期中数学(理)试卷
2017届江苏南通中学高三上期中数学(理)试卷河南省林州市第一中学2018届高三12月调研考试数学(文)试题(已下线)2017-2018学年第一学期期末复习备考之精准复习模拟题高三年级(文)人教版数学试题(B卷)江西省宜春市第九中学2018-2019学年高二下学期期中考试数学(文)试题福建省尤溪县2018-2019学年普通高中高三上学期半期数学(理)试题山东省济南市外国语学校2020-2021学年高二下学期5月月考数学试题
名校
9 . 在单调递增数列
中,
,且
成等差数列,
成等比数列,
.
(1)①求证:数列
为等差数列;
②求数列
通项公式;
(2)设数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5786daa387797fe28543eb25cdcf0193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48aa8f272b068a13e9a61912ed5697cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee635f30f8c1ab7cc90ca44ea5071f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd2bfef3925d6f9f46b96b301c58223.png)
(1)①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fffabc2dfb59ac198c06dbcadfa75c.png)
②求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.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/9fea6ba08b4985e51979378af23595d5.png)
您最近一年使用:0次
2016-12-04更新
|
970次组卷
|
4卷引用:2017届河北衡水中学高三上学期第二次调研数学(理)试卷
2017届河北衡水中学高三上学期第二次调研数学(理)试卷2016-2017学年湖北省孝感市七校教学联盟高一下学期期中考试数学(理)试卷河北省保定市定州中学2021届高三上学期期中数学试题(已下线)黄金卷13-【赢在高考·黄金20卷】备战2021年高考数学(文)全真模拟卷(新课标Ⅱ卷)
解题方法
10 . 等差数列
的前
项和为
,数列
是等比数列,且满足
,
,
,数列
的前
项和
,若
对一切正整数
都成立,则
的最小值为________ .
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f478acd1cb5b5a7f66d10b4f318d78d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab012ccad381f23d7796cd205eaa399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364f8ccb16e0dd0873291c9f351d6ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2767882820f4ba0defde0e412adb747f.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/7b7a1a4869a0329cdf22169ce8df5ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次