1 . 设正项数列
的前
项和为
,
,且满足_____.给出下列三个条件:
①
,
; ②
;
③
.
请从其中任选一个将题目补充完整,并求解以下问题.
(1)求数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1038200f2d97a52c716aab6c3bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceb2af10086d16399167b8f0181e17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e68f3125818585998b2a82f348cfd06.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c5da0a9c1708082a5716453236f77e.png)
请从其中任选一个将题目补充完整,并求解以下问题.
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d256cbf15595993837844a34cc56c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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
2024-03-31更新
|
456次组卷
|
5卷引用:福建省福州外国语学校2023-2024学年高二下学期4月期中考试数学试题
福建省福州外国语学校2023-2024学年高二下学期4月期中考试数学试题四川省南充高级中学2023-2024学年高二下学期第一次月考(3月)数学试题四川省成都市西北中学2023-2024学年高二下学期4月阶段性考试数学试题(已下线)模块四专题6重组综合练(四川)(8+3+3+5模式)(北师大版高二)单元测试B卷——第四章 数列
2 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,且数列
的前
项和为
,若
都有不等式
恒成立,求
的取值范围.
![](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/ae7436394b1aa194efb2dc97a953cbd9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.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/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f75ba8bc900ffb8d12a0923f7aa8285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-03-26更新
|
1379次组卷
|
5卷引用:福建省南平市2023-2024学年高二上学期期末数学试题
福建省南平市2023-2024学年高二上学期期末数学试题黑龙江省实验中学2023-2024学年高二下学期4月考数学试题(已下线)专题04数列求和的6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)(已下线)专题03数列期末7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(人教B版2019选择性必修第三册)江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
3 . 某工厂去年12月试产了1000个电子产品,产品合格率为0.85.从今年1月开始,工厂在接下来的一年中将生产这款产品,1月按去年12月的产量和产品合格率生产,以后每月的产量都在前一个月的基础上提高
,产品合格率比前一个月增加0.01.
(1)求今年2月生产的不合格产品的数量,并判断哪个月生产的不合格产品的数量最多;
(2)求该工厂今年全年生产的合格产品的数量.
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f733b1ceeead9ff892539d46a23f3626.png)
(1)求今年2月生产的不合格产品的数量,并判断哪个月生产的不合格产品的数量最多;
(2)求该工厂今年全年生产的合格产品的数量.
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884b9f6e9fde2b8951b4b0eb362a27f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac57d6b171ab6bf190b16f774e5688e.png)
您最近一年使用:0次
4 . 已知数列
为递增的等差数列,
为
和
的等比中项.
(1)求数列
通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de97c8b7edcdcadf6f00a8e026ce4774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5026cdcb467987cdef9da732a17582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea2059d41da264b08aa7692f82fc1fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
5 . 已知数列
的首项
,且满足
.
(1)判断数列
是否为等比数列;
(2)若
,记数列
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6309accb96679b392ed2d4631e21b749.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ae8af1b4dfc31c317fcbe291d28b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-03-06更新
|
1186次组卷
|
4卷引用:福建省福州市八县(市、区)一中2023-2024学年高二上学期期末联考数学试题
6 . 已知数列
的前
项积为
,且
.
(1)证明:
是等差数列;
(2)从
中依次取出第1项,第2项,第4项……第
项,按原来顺序组成一个新数列
,求数列
的前
项和.
![](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/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad36891d5193558a492a3d63713b2719.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe94bca98a93e4518303f78897c591e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af68ed265e5653abd5aa5c7109bbf54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-02-27更新
|
594次组卷
|
2卷引用:福建省福州第一中学2023-2024学年高三上学期期末考试数学试题
7 . 已知数列
的前
项和为
,且满足
,若数列
的前
项和
满足
恒成立,则实数
的取值范围为________ .
![](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/eb7d2d5c0e684bba3a14002fca76f40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.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/fafc4304a5f5c29fdf028f32a8c57f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 已知函数
满足
,数列
满足:
.
(1)求数列
的通项公式;
(2)数列
满足
,其前
项和为
,若
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f47a8dbff3f06c502f370e6961106da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b209230761fa07f63e4300b7f029429d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd2b2b1c9c82997b28888cef839e67b.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/27c93c6fb7f0a29fee41862aa7604470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-02-23更新
|
766次组卷
|
4卷引用:福建省龙岩市2023-2024学年高二上学期期末教学质量检查数学试题
福建省龙岩市2023-2024学年高二上学期期末教学质量检查数学试题四川省天府新区实外高级中学2023-2024学年高二下学期3月月考数学试卷(已下线)第一章数列章末十六种常考题型归类(3)(已下线)专题04数列求和的6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)
解题方法
9 . 已知数列
的前
项和为
,且
.
(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/8d3f217b40ce965450a2a7a706943d3d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.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)
您最近一年使用:0次
10 . 已知数列
满足:
.
(1)证明:数列
是等比数列,并求数列
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,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6591daffdf70265b0dc4b796775395b8.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](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/0526bcbb60d5258b461ab634e913212d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次