名校
1 . 已知数列
满足
,
.
(1)求证:
是等差数列,并求出数列
的通项公式;
(2)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/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b6829fea0e2efa76810d540738793f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.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/f052af7ec6eabf99cbea5543397cd1d5.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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2018-08-25更新
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3卷引用:江西省赣州市南康中学2017-2018学年高一下学期第三次月考数学(文)试题
名校
2 . 已知数列
满足
.
证明数列
为等差数列;
求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e604dec7d94d46b5a29f8bd84e995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
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2018-09-11更新
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8卷引用:江西省吉安市遂川中学2018-2019学年高一下学期第一次月考数学(理)试题
12-13高三上·安徽滁州·期末
3 . 已知数列
满足:
,
.
(1)若
,求证:数列
为等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629e54076b5754d3309da6cdcebfefc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2018-07-07更新
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3卷引用:【全国市级联考】江西省上饶市2017-2018学年高一下学期期末考试数学(文)试题
【全国市级联考】江西省上饶市2017-2018学年高一下学期期末考试数学(文)试题(已下线)2012届安徽省滁州中学高三上学期期末考试文科数学江苏省扬州市新华中学2020-2021学年高二上学期10月阶段性测试数学试题
名校
解题方法
4 . 已知数列
的前
项和
(
为正整数).
(1)求证:
为等差数列;
(2)求数列
的前
项和公式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54c4d2988c910f672fcf07fad4d8d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f2976eee7e397c5495831f10f83ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54c4d2988c910f672fcf07fad4d8d34.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d90fcbb1be182169160385ff14988ce.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54c4d2988c910f672fcf07fad4d8d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2018-03-09更新
|
890次组卷
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4卷引用:江西省上饶中学2018-2019学年高一下学期第一次月考数学(理科)试题
江西省上饶中学2018-2019学年高一下学期第一次月考数学(理科)试题广东省江门市2018届高三3月模拟(一模)考试数学理试题(已下线)2018年9月25日《每日一题》一轮复习(理)-数列的通项与求和(2)(已下线)2018年9月27日《每日一题》一轮复习(文)-数列的通项与求和(2)
5 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccb6fe23b7cd66910351efcbabd0d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad39387c7d2658d4e8dd4bb4d4962567.png)
(1)设
,证明数列
为等差数列,并求数列
的通项公式;
(2)求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccb6fe23b7cd66910351efcbabd0d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad39387c7d2658d4e8dd4bb4d4962567.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8049a7c9c5d4a9fe647cafde9175a366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
6 . 已知数列
,
,
为数列
的前
项和,
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe021309c7ea1e58d0b165f2c5eec94c.png)
.
(1)求数列
的通项公式;
(2)证明
为等差数列.
(3)若数列
的通项公式为
,令
.
为
的前
项的和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](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/9e78f07af568e395269122824300b039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe021309c7ea1e58d0b165f2c5eec94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eb761dbf1a5a1106dad1a25ce08a89.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092910e683ac87df1b7c643ca80e5c31.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771e7687d79e249a0b7b768220c61cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8c06db928acb22ff897b0710424d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d789051798795d5575d4c3896750e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2018-03-18更新
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8卷引用:江西省宜春市上高县第二中学2019-2020学年高一下学期期末考试数学(文科)试题
江西省宜春市上高县第二中学2019-2020学年高一下学期期末考试数学(文科)试题天津市滨海新区2017届高三上学期八校联考(理科)数学试卷广东省中山市第一中学2017-2018学年高二上学期第二次统测数学(理)试题广东省中山市第一中学2017-2018学年高二上学期第二次统测数学(文)试题辽宁省实验中学、大连八中、大连二十四中、鞍山一中、东北育才学校2017-2018学年高二上学期期末考试数学(文)试题福建省闽侯第四中学2017-2018学年高二上学期期末考试数学(文)试题陕西省黄陵中学2017-2018学年高二(普通班)下学期开学考试数学(文)试题重庆市缙云教育联盟2020-2021学年高二上学期10月月考数学试题
7 . 设正项数列
的前
项和为
,已知
,
,4成等比数列.
(1)求数列
的通项公式;
(2)设
,设
的前
项和为
,求证:
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23016d1186ebefd8d67387f43f100229.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/686ece75006ad358f23314dc8a246e11.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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2018-01-26更新
|
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2卷引用:江西省宜春市高安中学2019-2020学年高一下学期期中考试数学(B)试题
名校
8 . 已知等差数列
的公差
,其前
项和为
,若
,且
成等比数列.
(1)求数列
的通项公式;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd71318ddbb81a2d7ed7847e1ff744a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000d4da0e3bbb394cf8f3b072bdd7462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd36e98dd9c90af2da2f59007d07d349.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9799cb6368dbe814001ad31b0e8998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bebd7246a1a023a65cb9bdfeb8ea33.png)
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2018-05-12更新
|
2062次组卷
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13卷引用:江西省南昌市新建区第一中学2020-2021学年高一下学期第一次月考数学试题
江西省南昌市新建区第一中学2020-2021学年高一下学期第一次月考数学试题河北省滦州市第一中学2019-2020学年高一下学期期中数学试题【全国市级联考】河南省郑州市2018届高三第三次质量预测数学(理)试题(已下线)2018年高考题及模拟题汇编 【理科】4.数列与不等式(已下线)2018年高考题及模拟题汇编 【文科】4.数列与不等式陕西省延安市黄陵中学2018届高三(普通班)6月模拟考试数学(理)试题河南省郑州市第一中学2019-2020学年高三上学期期中考试数学(理)试题2020届山东省滕州市第一中学高三3月线上模拟考试数学试题(已下线)第7篇——数列-新高考山东专题汇编(已下线)专题7.4 数列求和(讲)-2021年新高考数学一轮复习讲练测(已下线)专题7.4 数列求和(精讲)-2021年新高考数学一轮复习学与练(已下线)专题7.4 数列求和(讲)- 2022年高考数学一轮复习讲练测(新教材新高考)福建省漳州市华安县第一中学2023-2024学年高二上学期第一次(10月)月考数学试题
2013·北京西城·二模
名校
9 . 已知等比数列
的各项均为正数,
.
Ⅰ
求数列
的通项公式;
Ⅱ
设
证明:
为等差数列,并求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad351b9fd1572a0bea733c69d6d4e9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2920ad541a6075bc4c0abb31b40691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
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2018-08-31更新
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12卷引用:【全国百强校】江西省南昌市第十中学2017-2018学年高一5月月考试数学(文)试题
【全国百强校】江西省南昌市第十中学2017-2018学年高一5月月考试数学(文)试题江西省南昌八中、南昌二十三中等四校2018-2019学年高一下学期期中联考数学试题云南省宾川县第四高级中学2017-2018学年高一5月月考数学试题重庆市南岸区2019-2020学年高一上学期期末数学试题(已下线)2013届北京市西城区高三二模文科数学试卷2020届陕西省西安中学高三第一次模拟考试数学(文)试题北京市第四中学2021届高三12月数学考试试题陕西省榆林市第十二中学2020-2021学年高三上学期12月第三次月考数学(文)试题河南省开封市2020-2021学年高二上学期五县联考期中数学(理)试题北京市第一七一中学2022届高三10月月考数学试题黑龙江省双鸭山市友谊县高级中学2022-2023学年高二上学期期末考试数学试题黑龙江省克东县第一中学、克东县职业技术学校2022-2023学年高二下学期3月质量监测数学试题
10-11高一下·江西上饶·阶段练习
解题方法
10 . 设数列
的各项都是正数,且对任意
,都有
,记
为数列
的前n项和
(1)求证:
;
(2)求数列
的通项公式;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d120f89f4304c3c710aecee01a54f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6947966790678dcf4a1c6b9d30f556b5.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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