1 . 已知数列
满足
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53271336649378a043f9da8b8bdc1cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-03-21更新
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5卷引用:山西省部分学校2021-2022学年高二下学期期中数学试题
名校
解题方法
2 . 设数列
的前
项和为
,且
.
(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/57c599e7cec6d192fb73218e7882ceca.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62305cda982dd4b73aec6983d3968c84.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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2021-11-23更新
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2卷引用:山西省怀仁市第一中学2022届高三上学期期中数学(理)试题
3 . 下列关于星星的图案构成一个数列
,
对应图中星星的个数.
![](https://img.xkw.com/dksih/QBM/2021/11/15/2851810368839680/2854510449860608/STEM/030afbbc01314705aef4781c151fcc8c.png?resizew=446)
(1)写出
,
的值及数列
的通项公式;
(2)求出数列
的前
项和
;
(3)若
,对于(2)中的
,有
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e94a3e7faa7b7215ea4457d86e0fa5.png)
![](https://img.xkw.com/dksih/QBM/2021/11/15/2851810368839680/2854510449860608/STEM/030afbbc01314705aef4781c151fcc8c.png?resizew=446)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7978e3c1522080083cb5de7d2cb25db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85883847ef20dcd71f835ed4a150309a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0010f17f7ae1fd17f739fea53f76083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4 . 已知数列
是各项均为正数的等差数列.
(1)若
,且
,
,
成等比数列,求数列
的通项公式;
(2)在(1)的条件下,数列
的前n项和为
,设
,若对任意的
,不等式
恒成立,求实数k的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547886abee1a603e275c6e808fb5b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在(1)的条件下,数列
![](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/e2b6f47f5e789d6c8ab0f9be98c35cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff23c92d09063516ab7a82d8bb9b77fd.png)
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2021-11-17更新
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5卷引用:山西省运城市2022届高三上学期期中数学(理)试题
山西省运城市2022届高三上学期期中数学(理)试题陕西省咸阳市武功县普集高级中学2022-2023学年高三上学期11月阶段性检测理科重点班数学试题陕西省咸阳中学2022-2023学年高二上学期期中理科数学试题(已下线)专题十九 数列的通项以及数列中的不等问题(已下线)思想03 运用函数与方程的思想方法解题(精讲精练)-1
解题方法
5 . 已知等比数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)若数列
满足:
,
,求
的前
项和.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207122b4594b80a670136d5194f74ba4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260febdc9f73fb2f57f26881e483d1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1a208706fe64c4a6709e9de5da2bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
6 . 如图所示将若干个点摆成三角形图案,每条边(包括两个端点)有
个点,相应的图案中总的点数记为
,则
( )
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723065982861312/2794726340395008/STEM/d25815ff-9b80-4e81-bfbb-b4770806dad6.png?resizew=488)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa07000929c95c721ae4fcbb314abd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed52e5cd3461f78bfe5644bb25d2d5e.png)
![](https://img.xkw.com/dksih/QBM/2021/5/17/2723065982861312/2794726340395008/STEM/d25815ff-9b80-4e81-bfbb-b4770806dad6.png?resizew=488)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:山西省怀仁市2020-2021学年高二下学期期中数学(文)试题
山西省怀仁市2020-2021学年高二下学期期中数学(文)试题贵州省遵义市2022届高三上学期第一次质量监测数学(文)试题(已下线)第01讲 数列-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第一册)
名校
解题方法
7 . 已知数列
满足
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项之和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ed76b5ad8b953d10139c874f6f1e6c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36925e53ab12172c7616b6d64b608b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf4cea13f3c0a934a3be5a3d834774f.png)
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2021-08-26更新
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4卷引用:山西省怀仁市2020-2021学年高二下学期期中数学(理)试题
8 . 已知数列
的通项公式为
,将这个数列中的项摆放成如图所示的数阵,记
为该数阵从左至右的n列以及从上到下的n行共
个数的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4981e081d6ffeb93fff67857011fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae9ec0b88b8d970e6ec951d21e3174e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc737d1bd1b5c09db046ae238aac6f32.png)
… … … … …
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60e0389684ef22db26141c22ae8374b.png)
(1)求
,猜想并写出
(直接写出);
(2)记
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760526364f3b888cbdc9193285e3c80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4981e081d6ffeb93fff67857011fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae9ec0b88b8d970e6ec951d21e3174e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc737d1bd1b5c09db046ae238aac6f32.png)
… … … … …
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60e0389684ef22db26141c22ae8374b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81808a0f8687cc51946a83f28b7e7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
9 . 已知数列
的通项公式为
,将这个数列中的项摆放成如图所示的数阵,记
为该数阵从左至右的n列以及从上到下的n行共
个数的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4981e081d6ffeb93fff67857011fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae9ec0b88b8d970e6ec951d21e3174e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc737d1bd1b5c09db046ae238aac6f32.png)
… … … … …
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60e0389684ef22db26141c22ae8374b.png)
(1)求
,猜想并写出
(直接写出);
(2)记
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4981e081d6ffeb93fff67857011fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae9ec0b88b8d970e6ec951d21e3174e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc737d1bd1b5c09db046ae238aac6f32.png)
… … … … …
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60e0389684ef22db26141c22ae8374b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99ed9d94718d293ddf4ea48ac03b286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e80983b88cdf6b540502816c87d13.png)
您最近一年使用:0次
10 . 已知正项数列
的前n项和为
,满足
(
,
),
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
的表达式.
![](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/7827282f47662d06d71699754ca7762e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f71d96b9ffbe5ce6e793cd0ecc862bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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2021-04-22更新
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11卷引用:山西省运城市2021届高三(上)期中数学(理科)试题
山西省运城市2021届高三(上)期中数学(理科)试题福建省福州第三中学2021届高三第一学期第六次质量检测数学试题(已下线)专题4.6 《数列》单元测试卷(B卷提升篇)-2020-2021学年高二数学选择性必修第二册同步单元AB卷(新教材人教A版,浙江专用)(已下线)第四章数列 核心专项练习-【提升专练】2021-2022学年高二数学新教材同步学案+课时对点练(苏教版2019选择性必修第一册)(已下线)考点24 已知递推公式求同通项公式求数列的通项公式-备战2022年高考数学(理)一轮复习考点帮(已下线)第四章 数列单元测试A卷-【新高考题型】2020-2021学年高二数学下学期单元实战演练AB卷(人教A版2019)河北省石家庄2022届高三上学期10月联考数学试题(已下线)综合复习与测试培优练习(卷一)-【提升专练】2021-2022学年高二数学新教材同步学案+课时对点练(苏教版2019选择性必修第一册)沪教版(2020) 选修第一册 领航者 第4章 4.4 每周一练(3)(已下线)第18节 等差数列及前n项和江西省宜春市万载中学2021-2022学年高一下学期第三次月考数学(文)试题