1 . 已知数列
,______.在①数列
的前n项和为
,
;②数列
的前n项之积为
,这两个条件中任选一个,补充在上面的问题中并解答.(注:如果选择多个条件,按照第一个解答给分.在答题前应说明“我选______”)
(1)求数列
的通项公式;
(2)令
,求数列
的前n项和
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f8c6e4c5cfd0abea0ab002ab1b6fda.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb4e138bca973f72f64014abe10237b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-03-19更新
|
504次组卷
|
2卷引用:北京市北京交通大学附属中学2023-2024学年高二下学期期中练习数学试题
解题方法
2 . 数列
的前
项和为
,且
,
,
,
,
,
.
(1)求
,
,
的值;
(2)求
的通项公式;
(3)设
,求
的表达式.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59557c76432f5350a610400e7ab8d27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
(1)求
![](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/daf464629fa321a6ff7401ab79f07083.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b858820c0024326c12d96d7302b47fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
为数列
的前
项和,满足
,则
的值为____________ .
![](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/4f5c678de58d5f9e11fd0bfc599e3cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
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2023-06-14更新
|
427次组卷
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3卷引用:北京市海淀区首都师范大学附属中学2022-2023学年高二下学期期中练习数学试题
名校
解题方法
4 . 已知数列
的前n项和为
,在条件①、条件②、条件③这三个条件中选择一个作为已知.
(1)求数列
的通项公式;
(2)若
是公差为2的等差数列,
,求数列
的前n项和
.
条件①:
且
;
条件②:
;
条件③:
.
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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f8833a02e108a41509ac655542dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1715b93a632f12897db3f060276588.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b75dbb20178da2eec9ff11a9c74e841.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e654568f7561197af8dac889750a86b.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
2023-06-14更新
|
260次组卷
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3卷引用:北京市怀柔区第一中学2022-2023学年高二下学期期中考试数学试卷
名校
5 . 设数列{
}的前
项和为
,且满足
.
(1)求证数列{
}是等比数列;
(2)数列
满足
,且
.
(i)求数列
的通项公式;
(ii)若不等式
对
恒成立,求实数λ的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/642e798608dc8e2d34948aec80798b5c.png)
(1)求证数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b754debcc24734559cb0f9684ac02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(ii)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4a04b36fe6e8c9d9b35e5073c7e483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f517647b99280339af20d18f4023a798.png)
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6 . 设首项是1的数列
的前
项和为
,且
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
______ ;若
,则正整数
的最大值是________ .
![](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/e571bbe8329c240f5f8abefb72b63fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2754a95bf12e58827090b6d41e19a2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-11-19更新
|
587次组卷
|
7卷引用:北京市通州区2022届高三上学期期中数学质量检测试题
名校
解题方法
7 . 若数列
的
项和为
且
,
,则下列说法不正确的是( )
![](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/5b8e34cdd334b668fe8ca80e133833b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
A.![]() | B.![]() |
C.数列![]() | D.数列![]() |
您最近一年使用:0次
8 . 已知数列
满足:
,
,
,数列
满足
,
,数列
的前
项和为
.
(1)求数列
的通项
.
(2)求证:数列
为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ced564150c49c1afbe3e23cbd540ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a9a0c97fd3a3699d2e389caf0db486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f83efca68bc470e464a97a7cd6222e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff708fbea7c09e6ef5346655e7e11c6.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)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79768a4e3970a18741cee3fbd8bcbdad.png)
您最近一年使用:0次
名校
9 . 已知数列
的前n项和为
,
,
,则
=( )
![](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/59557c76432f5350a610400e7ab8d27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-09-23更新
|
1307次组卷
|
30卷引用:北京市海淀区北京57中2016-2017学年高一下期中考试数学试题
北京市海淀区北京57中2016-2017学年高一下期中考试数学试题2015-2016学年浙江金华、温州、台州三市部分学校高一下期中数学卷河北省承德市实验中学2018届高三上学期期中考试数学(理)试题浙江省温州新力量联盟2019-2020学年高二上学期期中联考数学试题河北省唐山市遵化市2018-2019学年高一下学期期中数学试题2017届陕西省黄陵中学高三(重点班)4月月考(高考全国统一全真模拟二)数学(文)试卷黑龙江省鹤岗市第一中学2016-2017学年高一下学期期末考试数学(文)试题黑龙江省鹤岗市第一中学2016-2017学年高一下学期期末考试数学(理)试题【全国百强校】黑龙江省大庆中学2017-2018学年高一下学期期末考试数学试题【市级联考】河南省洛阳市2019届高三上学期尖子生第二次联考数学文科试题(已下线)2018年12月30日 《每日一题》(文数)人教必修5+选修1-1(高二上期末复习)-每周一测(已下线)专题6.1 数列的概念与简单表示法(讲)【文】—《2020年高考一轮复习讲练测》(已下线)2019年12月29日《每日一题》必修5+选修1-1文数-每周一测四川省仁寿第一中学北校区2020届高三下学期第二次高考模拟数学(文)试题四川省仁寿第二中学2020届高三第三次高考模拟数学(文)试题(已下线)题型09 求数列通项-2020届秒杀高考数学题型之数列四川省自贡市田家炳中学2020-2021学年高二上学期开学考试数学试题吉林省长春市第八中学2020届高三考前浏览卷数学(理)试题(已下线)专题16 数列的通项与求和-2020年高考数学(文)母题题源解密(全国Ⅰ专版)江西省南昌市第二中学2021届高三上学期第四次考试数学(理)试题江西省新余市第四中学2021届高三上学期第四次考试数学(理)试题陕西省咸阳市武功县2021届高三下学期第二次质量检测理科数学试题云南省昭通市昭阳区第一中学2019-2020学年高二6月月考数学(文)试题(已下线)考点14 数列的综合运用-备战2022年高考数学(文)一轮复习考点微专题辽宁省盘锦市高级中学2021-2022学年高三上学期9月月考数学试题甘肃省天水市第一中学2021-2022学年高二上学期第一学段考试数学试题苏教版(2019) 选修第一册 一蹴而就 高考模拟测试云南省昭通市永善、绥江县2021-2022学年高二上学期期末考试数学试题辽宁省朝阳市第二高级中学2021-2022学年高二下学期4月月考数学试题(已下线)专题2 等差数列与等比数列-学会解题之高三数学321训练体系【2022版】
10 . 已知数列
为等差数列,且满足
,
,数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)证明:
是等比数列,并求
的通项公式;
(3)若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5359c8fdc022d7044ffb6fdb291666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf86d176e66c7defe5a2543108e0769.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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad9f4c2dc01c8eda8d6da00ae25851a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28529c0bdef3454044e37c4c949ccc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-02-05更新
|
502次组卷
|
4卷引用:北京市第四十三中学2020-2021学年高二下学期期中考试数学试题