解题方法
1 . 对于数列
,设甲:
为等差数列,乙:
,则甲是乙的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f7a0a63fb0e4c1786daa94333c0bb1.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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解题方法
2 . 已知等差数列
的公差不为零,
成等比数列,且
.
(1)求数列
的通项公式;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18556fda4a825861f1170cdeb059ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde13a1d82174255f34cc22f8127787b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed1649f5841159746937938ab5562ac.png)
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3 . 在等差数列
中,
,公差为
,前
项和为
,当且仅当
时
取最大值,则
的取值范围_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dd3c3b45125d4b484e2894992610f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.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/08ec5d76db9bd05547932966c9913dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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2024-05-27更新
|
557次组卷
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27卷引用:2013-2014学年浙江省平阳中学高二下学期期末考试文科数学试卷
(已下线)2013-2014学年浙江省平阳中学高二下学期期末考试文科数学试卷2014年全国普通高等学校招生统一考试文科数学(江西卷)(已下线)2015届甘肃省兰州第一中学高三12月月考数学试卷2014-2015学年河南省郑州47中高二上学期第一次月考试理科数学卷2015-2016学年陕西省西安市第七十中学高二10月月考理科数学试卷2016-2017学年河南八市重点高中高二文上月考一数学试卷河北省石家庄市第一中学2017-2018学年高一下学期期中考试数学(理)试题河北省石家庄市第一中学2017-2018学年高一下学期期中考试数学(文)试题步步高高二数学暑假作业:【理】作业9 等差数列步步高高二数学暑假作业:【文】作业9 等差数列上海市格致中学2018-2019学年高二上学期第一次月考数学试题上海市吴淞中学2018-2019学年高三上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2017届高三上学期期中数学试题湖南省衡阳市耒阳市第二中学2019-2020学年高二上学期8月月考数学试题(已下线)题型04 等差数列前n项和最大最小问题-2020届秒杀高考数学题型之数列(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项河南省郑州市八校2020-2021学年高二上学期期中联考数学(文)试题人教A版(2019) 选择性必修第二册 过关斩将 第四章 数列 4.2 等差数列 4.2.2 等差数列的前n项和公式 第2课时 等差数列前n项和的综合运用 基础过关练四川省攀枝花市第十五中学校2021-2022学年高一下学期第一次月考数学试题(已下线)8.1 等差数列上海市建平中学2023届高三上学期11月月考数学试题河南省漯河市高级中学2023-2024学年高三上学期摸底考试数学试题河南省焦作市博爱县第一中学2023-2024学年高三上学期8月月考数学试题上海市洋泾中学2024届高三上学期开学考试数学试题(已下线)考点3 等差列的前n项和及其性质 2024届高考数学考点总动员【练】(已下线)专题05 数列小题(7类题型,文科)(已下线)模块二 类型5 思维漏洞类12个易错高频考点
解题方法
4 . 已知
的数列
满足
,
,
成公差为1的等差数列,且满足
,
,
成公比为
的等比数列;
的数列
满足
,
,
成公比为
的等比数列,且满足
,
,
成公差为1的等差数列.
(1)求
,
.
(2)证明:当
时,
.
(3)是否存在实数
,使得对任意
,
?若存在,求出所有的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111d1a60e77d0293acdc3ea1c647d892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7054cf2f1fefdcea1bb11d966cd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f339d05a6032c0ca8c4187e75d8ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c0a2ab7198ec8e80904285ca6eb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbbadf02a2855e91a86dedc7a98781a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/306f3c49c9e05cfafadff14fdf90c3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965e8beb4ffed1c9cb0110b7e3f580f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f51bf9165826c40663d01427c24aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c0ec55d00d28d1a877e6ea38d6cd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3875830b3121133833a3b45d3407b6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c881b38e5e74dba689507bde6dfa3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87d6c4b41cede82adf564ecb513f326.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b6c614a413bd1db7b6de3a8ff7e7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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解题方法
5 . 已知等差数列
的前
项和为
,且
,则
( )
![](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/dfbd106e520ebeaaa31b4c461535f233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3155398e77dcfb5fc463d589fef478c.png)
A.9 | B.10 | C.11 | D.12 |
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2024-05-12更新
|
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2卷引用:浙江省绍兴市2024届高三下学期4月适应性考试数学试卷
6 . 设数列
为等差数列,前
项和为
.
(1)求数列
的通项公式;
(2)设
的前
项和为
,证明:
.
![](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/1d70f81230f504b54007a05b64b72663.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d6968ee4cf919cea5d9bb309dfadc6.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/99b71dfb5c6c02fa99293d1e365ebc03.png)
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2024-05-11更新
|
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3卷引用:浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题
浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题(已下线)专题07 数列通项与数列求和常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
7 . 等差数列
的首项为正数,公差为
,
为
的前
项和,若
,且
,
,
成等比数列,则
( )
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f027fbe4d94609f66634d7c34a000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
A.1 | B.2 | C.![]() | D.2或![]() |
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解题方法
8 . 设等差数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e9d3644920a6654c41de61b7f3636d.png)
(1)求数列
的通项公式;
(2)已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4612f11b9f469586e9a432b233bd4696.png)
,记
的前
项和为
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/4f40ba28d4de58fa9602eb38608551cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2395ccadbeb8353ead0d573ca02c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e9d3644920a6654c41de61b7f3636d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4612f11b9f469586e9a432b233bd4696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de331418844737c645e505fa7fcd4ecb.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/fb3200f3cc24af2c9663b5c0de282810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
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|
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2卷引用:浙江省台金七校联盟2023-2024学年高二下学期4月期中联考数学试题
9 . 已知等差数列
的前
项和为
,满足
.等比数列
满足
.
(1)求
的通项公式;
(2)若
,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/ccee8415ae2461ba5999937817acf89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1647a00ce9ccc019a4212f7468c00a24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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10 . 已知公差不为0的等差数列
满足
成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb930b4b569676616f66f483fcef84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed77b69c02cb6ac309d113599e2062e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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