名校
解题方法
1 . 已知等差数列
的前n项和为
,且
,
;数列
的前n项和
,且
,数列
的
,
.
(1)求数列
、
的通项公式;
(2)若数列
满足:
,当
时,求证:
.
![](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/96a5b6435419ce6d567635aa6af9c5b1.png)
![](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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd31348b13b06b1befefd36b446db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bc2b05dc79b18ecb4ac3f9b5c492d4.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/a105071647a4efb5b5940f6bd35cf168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ad71b24b28e23d72066c98aa944930.png)
您最近一年使用:0次
2022-05-28更新
|
2806次组卷
|
7卷引用:江西省丰城中学2022-2023学年高二创新班上学期期中考试数学试题
江西省丰城中学2022-2023学年高二创新班上学期期中考试数学试题(已下线)第7讲 数列求和9种常见题型总结 (2)湖南省四大名校名师团队2022届高三下学期高考猜题卷(A)数学试题(已下线)2022年全国新高考Ⅰ卷数学试题变式题9-12题(已下线)专题27 数列求和-2(已下线)2022年全国新高考Ⅰ卷数学试题变式题17-19题河北省唐山市第一中学2022-2023学年高三上学期期中考试数学试题
名校
解题方法
2 . 已知等差数列
的公差为
,
,若分别从下表第一、二、三行中各取一个数,依次作为
,
,
,且
,
,
中任何两个数都不在同一列.
(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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afba6619728461766f9a23e35a74259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
第一列 | 第二列 | 第三列 | |
第一行 | 3 | 5 | 6 |
第二行 | 7 | 4 | 8 |
第三行 | 11 | 12 | 9 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacbb62ffa53d9576c9e01b9ebdae9b.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6828a1cf75f19bb74a0e0490bd65c168.png)
您最近一年使用:0次
2022-10-30更新
|
475次组卷
|
10卷引用:河北省石家庄二中实验学校2021-2022学年高二下学期4月月考数学试题
河北省石家庄二中实验学校2021-2022学年高二下学期4月月考数学试题广东省广州市番禺中学2021-2022学年高二下学期期中数学试题(已下线)第四章 数列单元检测卷(知识达标)-【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)河北省石家庄市2022届高三一模数学试题(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)(已下线)文科数学-2022年高考押题预测卷03(全国甲卷)贵州省贵阳市2023届高三上学期质量检测数学(文)试题贵州省黔南州2023届高三上学期质量监测数学(文)试题贵阳市2023届高三年级上学期质量监测数学(理)试题贵州省黔南州2023届高三上学期10月质量监测数学(理)试题
名校
解题方法
3 . 已知数列{an}(n∈N*)是公差不为0的等差数列,a1=1,且
,
,
成等比数列.
(1)求数列{an}的通项公式;
(2)设数列{
}的前n项和为Tn,求证:Tn<1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14771ad8f9fd441429ba43bf00ec794e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab0ddb0876fafbfb4dd8451f8b38c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221e08845f95c15b3ee8a64fc80ce234.png)
(1)求数列{an}的通项公式;
(2)设数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0d9f8bf8dd91d8cd659ce6fb9c80b8.png)
您最近一年使用:0次
2022-10-20更新
|
372次组卷
|
2卷引用:江苏省连云港市灌南高级中学2021-2022学年高二上学期期中数学试题
名校
解题方法
4 . 已知数列
满足
,且
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bdfd592f818d0fec5293076f6e7348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6246d3caa133d7449288206b880760.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2de4ff7eab82bdd9cf46dfa6e8a548.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/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
2022-10-13更新
|
464次组卷
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3卷引用:陕西省咸阳市永寿县中学2022-2023学年高二上学期月考(一)数学试题
5 . 等差数列
中,前三项分别为
,前
项和为
,且
.
(1)求
和
的值;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c569df5eb8367b2b3bd8177a381e008.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/937c6e4af2c30c5a66878baf582f3a4b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b74193c04dd5b9b389f93de59e2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e80983b88cdf6b540502816c87d13.png)
您最近一年使用:0次
6 . 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
,
为
的前
项和,求证:
.
![](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/2a18556fda4a825861f1170cdeb059ff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81c50676cbc29cfffdb62e15414c81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/6bad40ea8ed5619b07b43d4a037697dd.png)
您最近一年使用:0次
2022-07-10更新
|
635次组卷
|
2卷引用:河北省石家庄市十八中2022-2023学年高二下学期开学考试数学试题
7 . 已知等差数列
的前n项和为
,且
.
(1)求数列
的通项公式;
(2)证明数列
是等比数列;
(3)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f985f75343e19f4e1a0751bb3c894039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
8 . 已知在各项均不相等的等差数列
中,
,且
、
、
成等比数列,数列
中,
,
,
.
(1)求
的通项公式及其前
项和
;
(2)求证:
是等比数列,并求
的通项公式;
(3)设
求数列
的前
项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbcab0da135650f774f78156d1f61ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9aa8112c66efc096e04eb7a9b684af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求
![](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)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0791fc0d57d2e1b240c01d4c4901dadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9441abef0ca046aafd4ce2c91b93be1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
您最近一年使用:0次
2022-03-04更新
|
1162次组卷
|
5卷引用:高二数学开学摸底考01(江苏专用)-2023-2024学年高中下学期开学摸底考试卷
(已下线)高二数学开学摸底考01(江苏专用)-2023-2024学年高中下学期开学摸底考试卷天津市滨海新区七所重点学校2022届高三下学期毕业班联考数学试题天津市第三中学2022届高三下学期三模数学试题(已下线)6.4 求和方法(精练)(已下线)专题05 数列 第二讲 数列的求和(解密讲义)
解题方法
9 . 设数列
是等差数列,已知
,公差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
,
为其前
项和,且
,
,
成等比数列.
(1)求数列
的通项公式及
;
(2)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a6e6e2466cef863dd605a31c9bc2f3.png)
,证明:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6244222d8b4e21fc28c0454d0276a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a6e6e2466cef863dd605a31c9bc2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.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/e672c3d231081d12e44a4211e5ac60bf.png)
您最近一年使用:0次
名校
解题方法
10 . 已知数列
满足:
,且
.
(1)求证:
是等差数列,并求
的通项公式;
(2)是否存在正整数m,使得
,若存在,求出m的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ada5be4490611aae7f00f5e5988bd2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)是否存在正整数m,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fddf20dbe45c34efef5b2c3a709c0b.png)
您最近一年使用:0次
2022-05-26更新
|
1832次组卷
|
8卷引用:江苏省南通市通州区金沙中学2021-2022学年高二下学期6月调研考试数学试题
江苏省南通市通州区金沙中学2021-2022学年高二下学期6月调研考试数学试题(已下线)等差数列的概念(已下线)4.2.1 等差数列的概(2)(已下线)高二数学下学期第二次月考模拟试卷(选择性必修第二册,含数列和导数)-【题型分类归纳】2022-2023学年高二数学同步讲与练(苏教版2019选择性必修第二册)4.2.1 等差数列的概念练习海南省海南中学2022届高三下学期第九次月考数学试题辽宁省沈阳市第二十中学2022-2023学年高三上学期一模考试数学试题江西省抚州市金溪县第一中学2023届高三上学期11月段考数学(文)试题