1 . 设等差数列
的前n项和为
,且
,
.
(1)求
的通项公式.
(2)令
,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc8d9d9a64737c4b7eec64152a8074b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f807c6c7eb57aa251d8450357787b3e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77dcc7869cc8d64711a6593f55e5ad5.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/a54fbf9c064d2259638f751e77686269.png)
您最近一年使用:0次
2 . 已知等差数列
的公差为
,前
项和为
,现给出下列三个条件:①
,
,
成等比数列;②
;③
.请你从这三个条件中任选两个解答下列问题.
(1)求
的通项公式;
(2)若
,且
,设数列
的前
项和
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.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/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cb4485663835fc40a9cf82f491d5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e6faeb947f20b486c3c888f1cd7e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7061a937daa71bec578d89117a507ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.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/5428b5ba92348081c866a7bf500bd315.png)
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2022-12-29更新
|
1008次组卷
|
4卷引用:拓展二:数列求和方法归纳(3)
(已下线)拓展二:数列求和方法归纳(3)四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(理)试题四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题(已下线)技巧04 结构不良问题解题策略(精讲精练)-2
名校
解题方法
3 . 已知等差数列
的前
项和为
,首项为
,
.数列
是等比数列,公比
小于0,且
,
,数列
的前
项和为
,
(1)记点
,证明:
在直线
上;
(2)对任意奇数
恒成立,对任意偶数
恒成立,求
的最小值.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de34c34529c9725beacee13db7b4e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371473cfe69603fea1895c793219e3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18c9b373494f7eb0128748120c1fdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec0699dc1a6f668a50c3017116751e4.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)
(1)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5fe6bf7695ea9b0a129d9f01953360e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a2d3cd8e283ae9d04bee5ab2e0895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa0667ad7e7060032787706750f409e.png)
(2)对任意奇数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db29df7dc5fdc524c6de316ac2a04cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc489c026bcc13f539e1b22467ee8b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5eeaa30850a2dd1abcb46208ac8b6a2.png)
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4 . 已知数列
的前
项和为
,且
, .请在①
;②
成等比数列;③
,这三个条件中任选一个补充在上面题干中,并解答下面问题.
(1)求数列
的通项公式;
(2)若
,记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448d0f33a081274c3b63a118cbe31e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7afafc032b325d1d667ccedc5d1fd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df98ce180b9d9e1a83f2c1332e2da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fdd7c09570afa545088fef4a369057.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4dc1e086d4aea10107c65f825b72de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af0d8d4f6e5b80bcb510173c5802358.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/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
5 . 已知等差数列
满足
,
,等比数列
满足
,
.
(1)求数列
,
的通项公式;
(2)令
,求证:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11048bcd7cad7b3774ddcb390e60b909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0b17bd48d9a55db81678478989b264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c064aaef26ca94e1bc9734ea554045e.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/35d5b833b6788c8ad168a43be83f3da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db185aea0db9ddcf00ba8a177e3b3716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
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2022-11-24更新
|
893次组卷
|
3卷引用:第四章 数列(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教A版2019)
6 . 已知在等差数列
中,
.
(1)求数列
的通项公式;
(2)记数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558a5c8887f3fbbeab3fa75bda981aba.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](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/0031136b88c5c677de5ab4b3c74b7388.png)
您最近一年使用:0次
2023-08-20更新
|
395次组卷
|
2卷引用:贵州省黔西南州兴义市顶效开发区顶兴学校2022-2023学年高二下学期第三次月考数学试题
名校
解题方法
7 . 等差数列
的前n项和
满足
,数列
,
,
,…,
的前5项和为9.
(1)求数列
的通项公式;
(2)若数列
的前n项和为
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751859e4f0b1cb2c94fd5cca373de9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe164d8a8a4049e01565b576007651de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01416ee1d48b17f889e444b7eda99740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fc2a492c940b8dbd366407d6cfa06.png)
(1)求数列
![](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/a1cfd82db92ce3d23c88877ab6f837f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d06989f94a12a22b982c85443cfdd.png)
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2022-10-27更新
|
852次组卷
|
6卷引用:数列专题:数列求和的6种常用方法-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)
(已下线)数列专题:数列求和的6种常用方法-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)2017届山西省高三下学期名校联考数学(文)试卷(已下线)山西省2017届高三下学期名校联考数学(文)试题内蒙古集宁一中(西校区)集宁一中2020-2021学年高三上学期期中考试数学(文)试题内蒙古乌兰察布市集宁一中西校区2020-2021学年高三(上)期中数学(文科)试题山东省青岛市青岛第九中学2020-2021学年高三上学期期中数学试题
8 . 在①
;②
;③
这三个条件中任选一个,补充在下面问题中,然后解答补充完整的题目.
问题:已知等差数列
为其前n项和,若______________.
(1)求数列
的通项公式;
(2)设
,求证:数列
的前n项和
.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c599e7cec6d192fb73218e7882ceca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f98d7b96c519daa615975d5533c9248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8236c97d9f87ae91ecae8020b03d73a7.png)
问题:已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4930a369c43166fbb10757a42339ee7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2098dc91bf6491336ff649814cbf823f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d76c3eb0a07a827877d7a4dc306211.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2023-02-15更新
|
455次组卷
|
2卷引用:浙江省宁波市余姚市2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 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
10 . 已知等差数列
的前n项和为
,数列
是各项均为正数的等比数列,
,
.
(1)求数列
和
的通项公式;
(2)令
,求数列
的前n项和
;
(3)令
,数列
的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e79e4498b00abf4d9aabdc4d2f2bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f1f1fd8717203ae837d22aaf7f8361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e9b495d5b1619e6ed0912516ed86d7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7554176f48d9f042d96ec5a9e01f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733969643c55ec0ddfddd781a6545778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529538fd39fe317bd6cfe8e07fe3c998.png)
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3卷引用:天津市四校(杨柳青一中、咸水沽一中 、四十七中,一百中学)2020-2021学年高二上学期期末联考数学试题