名校
解题方法
1 . 已知二项式
的展开式中仅第5项的二项式系数最大,且第4项,第5项,第6项的系数成等差数列.
(1)求
和n的值;
(2)当
,
,
时,若
恰好能被6整除,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733917cece1f3c77ef307bc76745ff8f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b5471b5cd78e6b6ad2bb4a29a5b23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3b06aa0fa17a8b1e3c2123b2f8309c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2卷引用:湖北省黄冈市浠水县第一中学2023-2024学年高二下学期期末质量检测数学试题
名校
解题方法
2 . 在如图三角形数阵中,第n行有n个数,
表示第i行第j个数,例如,
表示第4行第3个数.该数阵中每一行的第一个数从上到下构成以m为公差的等差数列,从第三行起每一行的数从左到右构成以m为公比的等比数列(其中
),已知
,
,
.
(1)求m及
;
(2)记
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fac8f1b6ea4a6aa0333703434a5907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f296e18597d4a633f2a918848d448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca775b1febd3def72e08a12bca7e3367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8318b84a8cd7e21a8a45c5b5edfa703e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/97b09fd9-6bbf-47d8-82d4-10f1c0062b5a.png?resizew=178)
(1)求m及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164ae1d08f223df4fa8df94bad8edd57.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73356a54faed3ebc7347e4ceaf5b1544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
3 . 若数列
的前n项和为
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace3d2566719b644a75f576754b51d66.png)
A.数列![]() | B.数列![]() |
C.数列![]() | D.数列![]() |
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4 . 过圆
:
内一点
的2023条弦恰好可以构成一个公差为
(
)的等差数列,则公差
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10103248277cc0ef4ae2136b07a4ebc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758a8bbcb76c425086a92f133203a433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知数列
的前n项和为
,且
,
.
(1)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,在数列
中是否存在3项
,
,
(其中
成等差数列)成等比数列?若存在,求出这样的3项,若不存在,请说明理由.
![](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/beb08c935c5a6dae2b2e53cfa8eac740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)求数列
![](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/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8598379ec01edc16c72c1d3fa3ce81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904e7018ec79c8b0efdcb3ba67cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2554efe1860dc6c769c34d8cfa6de3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7955013519718c9ac993531062495e95.png)
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6 . 设数列
的前n项和为
,
,则下列说法正确的是( )
![](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/e9ba984e922424ae65819c8a2bc27c64.png)
A.![]() |
B.当且仅当![]() ![]() |
C.![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 已知数列
的前n项和为
.
(1)求证:数列
是等差数列;
(2)设
的前n项和为
;
①求
;
②若对任意的正整数n,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/404378873d8f90e59cac43dbe6bb1562.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4689920e36d2ac304503d852083b07a4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb5d73cea14ac60937f8d5a4f5f0c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
②若对任意的正整数n,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6abf942265247031ce354221f22ac6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 在等差数列
中,
是
的前
项和,满足
,
,则有限项数列
中,最大项和最小项分别为( )
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e585900bbcf9f9e4dbba51a05225ead9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c596d3b2a629ecec71fc227a5bbbf1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e8afd6c4b50076b795e06da6462eb2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
9 . 已知等差数列
满足
,
.
(1)求
的通项公式;
(2)设数列
的前
项和为
,且
,若
,求正整数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917bba825d0d78ca5bd81606860b01ef.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/a49a13006ad16dd9d20a31b05f24ab87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84c2e653cea191505bce360c63ed525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 已知等比数列
前四项和为30,且
.
(1)求数列
的通项公式;
(2)在
和
之间插入1个数
,使
、
、
成等差数列;在
和
之间插入2个数
、
,使
、
、
、
成等差数列;
;在
和
之间插入
个数
、
、
、
,使
、
、
、
、
、
成等差数列.
①若
,求
;
②若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fb4b599e37a825bce2a0c29f09af8d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84bbc85887baf2c01afa80b0d5cc24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84bbc85887baf2c01afa80b0d5cc24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](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/1a558b61154c775d249113804c1453f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c4bd1eb1fa1f4fdc8392b59e6b6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a558b61154c775d249113804c1453f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c4bd1eb1fa1f4fdc8392b59e6b6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3633c588b06d9b188a4a11ce7cd9708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848016fb3db5063e4a51a64f920c7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044f1ac627493f30faee4f13c5a55ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3633c588b06d9b188a4a11ce7cd9708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848016fb3db5063e4a51a64f920c7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044f1ac627493f30faee4f13c5a55ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675524b0f1b2fd98800242ef6afc2b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5e416f18fe8bd5b7959a1b4b398400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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