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)
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2024-03-31更新
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5卷引用:单元测试B卷——第四章 数列
单元测试B卷——第四章 数列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)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
解题方法
2 . 已知公比不为1的等比数列
满足
,且
是等差数列
的前三项.
(1)求
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239e5d8c04dc3abd5e54f4caf2cbd0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66f5fba963e0530102ca629344b7ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2024-01-31更新
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7卷引用:第一章 数列(单元基础检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)
(已下线)第一章 数列(单元基础检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)河南省部分名校2023-2024学年高二上学期1月期末考试数学试题河南省濮阳市2023-2024学年高二上学期期末考试数学试题河南省周口市沈丘县第三高级中学2023-2024学年高二上学期期末数学试题(已下线)1.3.1 等比数列7种常见考法归类(3)(已下线)专题5-3数列求和及综合大题归类-1安徽省六安市田家炳实验中学2023-2024学年高二下学期开学测试数学试题
名校
解题方法
3 . 已知等差数列
的首项为1,公差
.数列
为公比
的等比数列,且
成等差数列.
(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/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e052d771d2875acb2756f4d5c118aee.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/8a68ca53ab0a60f6e817e9b2f3f769c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
您最近一年使用:0次
名校
解题方法
4 . 已知在等差数列
中,
,
,
是数列
的前
项和,且满足
.
(1)求数列
和
的通项公式;
(2)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07953530e3c248b3438fb200fb1661.png)
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d5c9abd937e015219fb01194ea74f0.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796e7e3214744fb50fc356441f2628fa.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07953530e3c248b3438fb200fb1661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bc2b05dc79b18ecb4ac3f9b5c492d4.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
2024-01-26更新
|
1573次组卷
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4卷引用:第一章 数列(单元综合检测卷) -2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)
(已下线)第一章 数列(单元综合检测卷) -2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)山西省太原市2024届高三上学期期末学业诊断数学试题浙江省嘉兴市第一中学2024届高三第一次模拟测试数学试题(已下线)4.3.2 等比数列的前n项和公式——随堂检测
5 . 已知数列
满足
.
(1)证明数列
为等差数列,并求
;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f143e51df4a96c7f3cdefa308d4576.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求数列
![](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)
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4卷引用:第五章:数列(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)
(已下线)第五章:数列(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)广东省深圳市龙岗区2023-2024学年高二上学期1月期末质量监测数学试题广东省广州市广东实验中学2024届高三上学期第二次调研数学试题江苏省南京市田家炳高级中学2023-2024学年高二下学期期中考试数学试卷
6 . 已知数列
的首项
,前n项和为
,且
.设
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082d2b4a888760653d2a76476d485078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d4fea9c27f8bb8f858855a659c346e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cb91e89800a81f4d62ed75c3ace24a.png)
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3卷引用:第五章:数列(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)
(已下线)第五章:数列(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)江苏省扬州市2023-2024学年高二上学期1月期末数学试题广东省广州市仲元中学2024届高三第二次调研数学试题
7 . 已知数列
满足
.
(1)证明
是等比数列,并求
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a36d69dbdcafadadb699b9c2f15606.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a30d759211e7f051fcf476ca07fa19.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
23-24高二上·江苏·课前预习
8 . 在等比数列
中.
(1)若它的前三项分别为5,-15,45,求
;
(2)若an=625,n=4,q=5,求
;
(3)若a4=2,a7=8,求an.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
(1)若它的前三项分别为5,-15,45,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3360bf86e9905c1af1cd0808a350ba.png)
(2)若an=625,n=4,q=5,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d049741bf0b2dcde76e4d1c524b9f5c9.png)
(3)若a4=2,a7=8,求an.
您最近一年使用:0次
2024-01-15更新
|
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4卷引用:第一章 数列(单元综合检测卷) -2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)
(已下线)第一章 数列(单元综合检测卷) -2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第二册)(已下线)第四章 数列(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第一册)四川省成都市新津区成外学校2023-2024学年高二下学期3月月考数学试题江西省上饶市余干县私立蓝天中学2023-2024学年高二下学期第一次月考数学试题
23-24高二上·江苏·单元测试
解题方法
9 . 数列
的前n项和为
,
,且
成等差数列.
(1)求
的值;
(2)证明
为等比数列,并求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70cb7b6d14630288595af4d9ad841312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50ded5e69df7d9af1e74a35e99b53ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4b18228a42cffd0e69c9ad215faffe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d049741bf0b2dcde76e4d1c524b9f5c9.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b821bbfe9a597a96f281d603b9579e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
您最近一年使用:0次
23-24高二上·上海·期末
名校
10 . 如果无穷项的数列
满足“对任意正整数
,都存在正整数k,使得
”,则称数列
具有“性质P”.
(1)若数列
是等差数列,首项
,公差
,判断数列
是否具有“性质P”,并说明理由;
(2)若等差数列
具有“性质P”,
为首项,
为公差.求证:
且
;
(3)若等比数列
具有“性质P”,公比为正整数,且
这四个数中恰有两个出现在
中,问这两个数所有可能的情况,并求出相应数列首项的最小值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320e7710ac9aafc0ecaf91ba6686cea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4654db8df46552ead8781a1dd2f06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029b5231e8dcc6c5b9bf324de42d301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2572192cc7ca046e9a3155ef3e56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3068733ef2ceda9f1620d5c9bcdfa542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e68eb4ade6e22982d2df5102d8894.png)
(3)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195d74fd21d66a2f647aa4363c1d8f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-01-14更新
|
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4卷引用:第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)2024届高三新改革适应性模拟测试数学试卷六(九省联考题型)黑龙江省牡丹江市第一高级中学2023-2024学年高二下学期开学考试数学试题