1 . 设数列
的前
项和为
,
,
,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/eba83359167d8ca8c9eafa8a23f34a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acac0a395f2315fdfe7014548dbc033.png)
A.![]() | B.![]() |
C.对任意的![]() ![]() | D.对任意的![]() ![]() |
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2024高二下·北京·专题练习
解题方法
2 . 北京天坛的圆丘坛为古代祭天的场所,分上、中、下三层.上层地面的中心有一块圆形石板(称为天心石),环绕天心石砌9块扇面形石板构成第一环,向外每环依次增加9块.下一层的第一环比上一层的最后环多9块,向外每环依次也增加9块.已知每层环数相同,且上、中下三层共有扇面形石板(不含天心石)3402块,则中层共有扇面形石板( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/b2c4d673-9d2d-4325-aa5f-d71bab93ca33.png?resizew=185)
A.1125块 | B.1134块 | C.1143块 | D.112块 |
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名校
解题方法
3 . 记
为数列
的前
项和,已知对任意的
,
,且存在
,
,则
的取值集合为______ (用列举法表示)
![](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/deda945164283569437cda6976fe35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194463e3b011603ff59c0789bcb65c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9cb7258cff29fdc988476f2087e7103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441f0c1f9853bc3104d1ff4cde2a79b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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2022-11-12更新
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1055次组卷
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6卷引用:江苏省南通市海安市2022-2023学年高三上学期11月期中数学试题
江苏省南通市海安市2022-2023学年高三上学期11月期中数学试题上海市高桥中学2022-2023学年高二上学期期末数学试题(已下线)模块二 数列 不等式-3江苏省无锡市南菁高级中学2023-2024学年高二上学期期末模拟数学试题江苏省盐城市射阳中学2023-2024学年高二上学期期末数学试题(已下线)4.1 等差数列(第1课时)(十大题型)(分层练习)-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)
名校
4 . 已知
,
,…,
(n为正整数)是直线
上的n个不同的点,设
,当且仅当
时,恒有
(i和j都是不大于n的正整数,且
),
.有下列命题:
①数列
是等差数列;
②
;
③点P在直线l上;
④若
是等差数列,P点坐标为
.
其中正确的命题有___________ .(填写所有正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042f6277c98e108cab95992342e4bfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09490514476657414d8991d633c9d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c5b2ecf3d4a067272790f360b5d05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47de6409d3ff5da9560329819eba385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9080a7449480ea117e133abce07db351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8db49d097b26af86f50bd45d4601a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614dff0cb877d00d301584ccb5dbccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7575f3f157337fa0a1eb565ad49a33.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496df17ad7e5c372200aa5cdcf2e093f.png)
③点P在直线l上;
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dc4024dd556d444a0668ebcbbe328b.png)
其中正确的命题有
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2022-01-21更新
|
886次组卷
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3卷引用:上海市复兴高级中学2021-2022学年高二上学期期末数学试题
上海市复兴高级中学2021-2022学年高二上学期期末数学试题(已下线)一轮复习适应训练卷(3)-2022年暑假高二升高三数学一轮复习适应训练卷(全国通用)上海市松江二中2021-2022学年高二下学期期末数学试题
13-14高一下·重庆·阶段练习
5 . 将一个等差数列依次写成下表:
第1行:2
第2行:5 8 11
第3行:14 17 20 23 26
………………………………………………
第
行:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e843a95617ad24ea4e789a0cdc5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c82be573157fd2c8068cb000505b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec8aa05d77a638e99494af9dfc0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e338a2cd8381353173126753e2415.png)
………………![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2814549b2e9f30007ab2d811dd9adf9.png)
(其中
表示第
行中的第
个数)
那么第
行的数的和是_________________ .
第1行:2
第2行:5 8 11
第3行:14 17 20 23 26
………………………………………………
第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e843a95617ad24ea4e789a0cdc5912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c82be573157fd2c8068cb000505b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aec8aa05d77a638e99494af9dfc0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e338a2cd8381353173126753e2415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392546a6637cb8faf9f356f4739cd7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2814549b2e9f30007ab2d811dd9adf9.png)
(其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee641d39bc70aa40e611fcfc6b78f30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
那么第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2012·上海徐汇·一模
名校
6 . 如果存在常数
,使得数列
满足:若
是数列
中的一项,则
也是数列
中的一项,称数列
为“兑换数列”,常数
是它的“兑换系数”.
(1)若数列:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b50284b0058b20b7ae5e63db2e47e7.png)
是“兑换系数”为
的“兑换数列”,求
和
的值;
(2)已知有穷等差数列
的项数是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
,所有项之和是
,求证:数列
是“兑换数列”,并用
和
表示它的“兑换系数”;
(3)对于一个不小于3项,且各项皆为正整数的递增数列
,是否有可能它既是等比数列,又是“兑换数列”?给出你的结论,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53f3ed849beaa4b8b2b22baf49055b4.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
(1)若数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b50284b0058b20b7ae5e63db2e47e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aab2189a2ba339749cdc8b7e96b357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知有穷等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5d534dadff2c6feaca4060ea972ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)对于一个不小于3项,且各项皆为正整数的递增数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2016-12-01更新
|
1376次组卷
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3卷引用:2012届上海市徐汇区高三4月学习能力诊断理科数学试卷