名校
解题方法
1 . 若一列不全为零的数除了第一个数和最后一个数外,每个数都等于与它相邻的前后两数之和,则称这列数具有“波动性质”.已知一列数共有2025个,第五个数为3,且具有“波动性质”,则这2025个数的和是__________ .
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2 . 若项数为
的数列
满足:
我们称其为
项的“对称数列”.例如:数列
为
项的“对称数列”;数列
为
项的“对称数列”.设数列
为
项的“对称数列”,其中
是公差为
的等差数列,数列
的最大项等于
,记数列
的前
项和为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07af7b0973d39dc2fa6fd75771df9314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a5108cea1d8f461cd2feb1976bb240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca5ed80b095dbf697beb2f091c3dbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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2023-09-04更新
|
384次组卷
|
3卷引用:专题09 数列的通项公式、数列求和及综合应用(练习)-2
(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2山东省淄博市实验中学、齐盛高中2023届高三上学期11月第一次模块考数学试题山东省潍坊市安丘市第一中学2023-2024学年高三上学期9月月考数学试题
解题方法
3 . 如果一个数列从第二项起,每一项与它前一项的差都大于2,则称这个数列为“
数列”.已知数列
满足:
,
,则数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
___________ ;若
,
,且数列
是“
数列”,则t的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf1b5b5f5f9269db4e3f748bd7f5348.png)
![](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/02ce9d5623b21817dd182b9058dc271a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e657ce17ffee05d4b7589961e50cedd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61943cdc3c6c702fbff21422f83d0cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf1b5b5f5f9269db4e3f748bd7f5348.png)
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名校
解题方法
4 . 已知数列
满足:
,
,若取整函数
表示不小于
的最小整数(例如:
,
),设
,数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38876b778335e9106f3146b894666542.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9362590b67bd4c13cb149878d5ca15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e888a9d26291b7867e878356f96eab2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f31ca87d5a5ffbc50b82ed8397cb5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c853e4033bc416435a3e8316a6723970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9feb047004eb507de484a7f8c5b6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036cb05aa65cff20c657ed53b38c5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13892e1c5a8b5fe216a91f598d677f67.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/38876b778335e9106f3146b894666542.png)
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5 . 设
,记最接近
的整数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1f8a7b246e790a7d32dbd6ef704360.png)
__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddb9f59ac6af99a8e1db5c320b47fe0.png)
__________ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4db1c3ec4c768e197b3a241b9737ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a5804538dc695f3d8fc9491f19a771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1f8a7b246e790a7d32dbd6ef704360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddb9f59ac6af99a8e1db5c320b47fe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2021-05-29更新
|
1259次组卷
|
8卷引用:第4章《数列》 培优测试卷(二)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
(已下线)第4章《数列》 培优测试卷(二)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)(已下线)专题08 数列-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)热点07 数列与不等式-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)模拟冲刺过关试卷03-【查漏补缺】2022年高考数学三轮冲刺过关(新高考专用)(已下线)重难点08 七种数列数学思想方法-2湖北省武汉市华中师范大学第一附属中学2021届高三下学期5月高考押题卷理科数学试题(已下线)湖北省武汉市华中师范大学第一附属中学2021届高三下学期5月高考押题卷文科数学试题广东省2022届高三上学期调研仿真数学试题
解题方法
6 . “0,1数列”在通信技术中有着重要应用,它是指各项的值都等于0或1的数列.设A是一个有限“0,1数列”,
表示把A中每个0都变为1,0,1,每个1都变为0,1,0,所得到的新的“0,1数列”,例如
,则
.设
是一个有限“0,1数列”,定义
,k=1,2,3,….若有限“0,1数列”
,则数列
的所有项之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e3d87be9f706832ef25537d78a201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e502eff0c1fe80b2a546ea4af17a9755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde81bb00224b2a80ba56c6ce27b94a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f939918bc9c36dbb32e8e1d7853b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374de27c75bc2269806d5b44d1518c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb23814c40a4929a6483d60a413968da.png)
您最近一年使用:0次
2022-04-08更新
|
790次组卷
|
4卷引用:第38练 等比数列
2023高三·全国·专题练习
7 . 对于数列
,定义
,称新数列
为数列
的一阶差分数列;定义
,称新数列
为数列
的二阶差分数列.若
,则称数列
是二阶等差数列.已知
是二阶等差数列,
,
,
,则数列
的通项公式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae54d34988f206ba259a3ee508d4bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761e8b5abba683b70f2c780188af5dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad312b3184102073385e95704dac84d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75864f4ce5169f86e7be36208871295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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解题方法
8 . 已知数列
的前n项和为
,数列
是首项为
,公差为
的等差数列.
表示不超过x的最大整数,如
,则数列
的前35项和为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0336731988224293bc0e9a7958adfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815ca11055d4b331e0c01f345a512c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19346ef0a606f0602acc0e40b7c01f46.png)
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2022-01-29更新
|
765次组卷
|
5卷引用:第02讲 等差数列(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)
(已下线)第02讲 等差数列(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)湖南省湖湘名校联盟2021-2022学年高二上学期期末联考数学试题湖南省湘潭市湘潭县2021-2022学年高二上学期期末数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)山西省朔州市怀仁市第一中学校等学校2024届高三上学期摸底数学试题
名校
9 . 在一个数列中,如果每一项与它的后一项的和为同一个常数,那么这个数列称为等和数列,这个常数称为该数列的公和.已知数列
是等和数列,且
,
,则这个数列的前2021项的和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc92d25b640d69069ebdeb3bd660650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d542d4679d36cc6f9f6a1d5aced714e.png)
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名校
解题方法
10 . 定义n个正数
的“均倒数”为
,若各项均为正数的数列
的前n项的“均倒数”为
,则
的值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa319dc8a88996be6eeb1053b635dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e0edbff1a6058758a281b1d6a9d017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72975772820e2660bf223a088d80116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88126c3cbc88e03d38f56b7da315b6.png)
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2022-11-28更新
|
724次组卷
|
4卷引用:专题04 数列的通项、求和及综合应用(精讲精练)-4
(已下线)专题04 数列的通项、求和及综合应用(精讲精练)-4河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题宁夏吴忠市吴忠中学2022-2023学年高二上学期期末考试数学(理)试题黑龙江省哈尔滨师范大学青冈实验中学校2023-2024学年高二下学期开学考试数学试题