1 . 已知
是等差数列
的前
项和,且
.
(1)求数列
的通项公式;
(2)若对任意
,求
的最小整数值.
![](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/78c6bc8b7800aecf6c5c217e12c4be6b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc7eeaa9e8c18d644d32c964144e63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 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
为等差数列
的前n项和,若 .
(1)求数列
的通项公式;
(2)设
,求数列
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/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfd6e425411179e2a5a06d84978356e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e26faf2d524402fefa06823506d1971.png)
问题:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfa94ec4beb4aeeb29eada00895ba4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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
解题方法
3 . 已知数列
满足
.
(1)求
;
(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/993f96653875fa66c34db65654480c62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2024-01-13更新
|
752次组卷
|
4卷引用:云南省玉溪市2023-2024学年高二上学期期末教学质量检测数学试卷
云南省玉溪市2023-2024学年高二上学期期末教学质量检测数学试卷(已下线)5.2.1 等差数列(4知识点+8题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)1.2.1 等差数列的概念及其通项公式8种常见考法归类(3)(已下线)专题01求数列通项公式9种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
2023·江苏南通·模拟预测
名校
解题方法
4 . 已知等差数列
的首项为1,公差为2.正项数列
的前
项和为
,且
.
(1)求数列
和数列
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/034ba25825c13725931c483aa47c9363.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/1ce8a818757319ec58ac08626462b46a.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ccf0c7c9a5dc2817ea92f2b5dd6f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
2023-12-25更新
|
2688次组卷
|
7卷引用:云南省玉溪第一中学2023-2024学年高二下学期第二次月考数学试题
云南省玉溪第一中学2023-2024学年高二下学期第二次月考数学试题(已下线)江苏省南通市如皋市2024届高三上学期教学质量调研(三)数学试题(已下线)模块三 专题7 大题分类练(数列)基础夯实练 期末终极研习室(高二人教A版)(已下线)专题04 数列通项与求和技巧总结(十大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)陕西省西安中学2024届高三模拟考试(一)数学(理科)试题(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)题型17 5类数列求和
5 . 已知正项数列
满足,
,且
.
(1)求数列
的通项公式;
(2)在
与
之间插入n个数,使这
个数组成一个公差为
的等差数列,若
,求证:
.
![](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/c16ee9b612e1345f2fbff2625688a5e5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f279786786fe8ad2438bec738d6ea905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36815c5c63a7b8b79974595f4149e292.png)
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2023-04-09更新
|
421次组卷
|
2卷引用:云南省玉溪第一中学2022-2023学年高二下学期第一次月考数学(文)试题
6 . 在①
,②
这两个条件中选择一个补充在下面的问题中,然后求解.
设等差数列
的公差为
,前n项和为
,等比数列
的公比为q.已知
,
, .
(说明:只需选择一个条件填入求解,如果两个都选择并求解的,只按选择的第一种情形评分)
(1)请写出你的选择,并求数列
和
的通项公式;
(2)若数列
满足
,设
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d61a111ab981437a0f71e6b063d8185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581e74360d31e2038bde239255bdbf69.png)
设等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc70c2154b22590c91d9a23e47b5160b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751859e4f0b1cb2c94fd5cca373de9af.png)
(1)请写出你的选择,并求数列
![](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/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ea1675261a5929c77af42bd9a9d1ac.png)
您最近一年使用:0次
2023-02-15更新
|
680次组卷
|
4卷引用:云南省玉溪市2023届高三毕业生第一次教学质量检测数学试题
解题方法
7 . 已知数列
满足
,
.
(1)证明
是等差数列;
(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/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572ce65d9bd2d43ac37e77d961a02c7d.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade1c9bd315cf48ebdd36af8ad552ec7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191274f45728789a84ce14ec0529aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021·全国·模拟预测
8 . 已知数列
是公差为2的等差数列,数列
是公比为2的等比数列.
(1)求数列
的通项公式;
(2)记
,且
为数列
的前n项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7695d7b6905ff9d4cd9b063028cc092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266fc958691f1d19699de3b9045402bd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807f2aebeabfbd6e5761205e8e659af5.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/aa33d6f116c61ab89224c1a9886861cd.png)
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2021-12-30更新
|
821次组卷
|
4卷引用:云南省玉溪第一中学2021-2022学年高二下学期期中考试数学试题
云南省玉溪第一中学2021-2022学年高二下学期期中考试数学试题(已下线)2022年全国高中名校名师原创预测卷(一)四川省阿坝藏族羌族自治州茂县中学2022-2023学年高二上学期入学考试数学试题第一章 数列 A卷基础夯实
9 . 已知点
(
)在函数
的图象上,
.
(1)证明:数列
为等差数列;
(2)设
,记
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3842e1ef6d2d1e38935834dbf62df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec1625aea1be225b03e444da4134197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c202d45733e28651b6e2aea9e6166295.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aee77a009ab8b5d553a0c765d2be881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac96b09d3eccdb9a4c17ecbdec9ecebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
10 . 已知
是公差不为零的等差数列,
是
和
的等比中项.
(1)求数列
的通项公式;
(2)令
,设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c7aeda228d8fb46f59a649f8e197f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d44ddab6e0c60119be69985ae7fa65b.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)
您最近一年使用:0次
2021-07-29更新
|
361次组卷
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3卷引用:云南省玉溪市2020-2021学年高二下学期期末数学(理)试题
云南省玉溪市2020-2021学年高二下学期期末数学(理)试题四川省广安市武胜烈面中学校2021-2022学年高二上学期数学(理)入学考试试题(已下线)河北省石家庄市河北省实验中学2024届高三上学期名校联考数学试题变式题15-18