1 . “中国剩余定理”又称“孙子定理”,原文如下:今有物不知其数,三三数之剩二(除以3余2),五五数之剩三(除以5余3),七七数之剩二(除以7余2),问物几何?现有这样一个相关的问题:已知正整数
满足三三数之剩二,将符合条件的所有正整数
按照从小到大的顺序排成一列,构成数列
,记数列
的前
项和为
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0966ebfd14ab7d6c6645c00d1fb2be95.png)
A.19 | B.17 | C.16 | D.15 |
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2 . 已知等比数列
的公比为
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d6f2badbd8d89c8248187347ada7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29db33eb9dc2cb64ee0299eee7ef8f7.png)
A.9 | B.6 | C.12 | D.8 |
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2卷引用:河北省石家庄十五中2023-2024学年高二下学期期中数学试题
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3 . 已知非零实数a,b,c不全相等,则下列结论正确的是( )
A.若a,b,c成等差数列,则![]() ![]() ![]() |
B.若a,b,c成等比数列,则![]() ![]() ![]() |
C.若a,b,c成等差数列,则![]() ![]() ![]() |
D.若a,b,c成等比数列,则![]() ![]() ![]() |
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2卷引用:广东省佛山市南海区第一中学2023-2024学年高二下学期阶段三暨期末统考模拟检测数学试题
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4 . 记
为等差数列
的前n项和,若
,
,则
的公差为( )
![](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/a75739be7640de2ab1c3e191b9857a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba339ce7b73e22ac17eb97ab975a41ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.-4 | B.-2 | C.2 | D.4 |
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2卷引用:广东省佛山市南海区第一中学2023-2024学年高二下学期阶段三暨期末统考模拟检测数学试题
5 . 若数列
满足
(
且
),
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b441801f91e31f4fb4b9bd6e2dcf763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b95079ade5ac98fc651fafc489761f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知数列
满足
,
,则数列
的前9项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec499e8ee1735a250346620c50f588a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.6 | B.![]() | C.3 | D.![]() |
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7 . 在等差数列
中,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fb3634ef6515ebb1db5df9208a9f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6832051de5898c8540b448f73eb3795c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
A.4 | B.5 | C.6 | D.8 |
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8 . 过圆
外一点
做圆
的切线
,切点为
,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e0db273061d0331e4e5da9ff1e955e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b0dd09a59056af579586ab8b69f4f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817a48b819ab971e79bad7b20250294.png)
A.![]() | B.![]() | C.![]() | D.8 |
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9 . 已知正项等比数列
的前
项和为
,若
,则数列
的公比为( )
![](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/cb88f094800881efbb8cb83b5abf5a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() | B.![]() | C.2 | D.![]() |
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10 . 若
,
,且
,则下列不等式一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb78d20cf8bb76cd3cbe6275ffa4053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1de5fcd3122443699a9f574a8396b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574b3c0cdd4e1c6f3c77d43dc7e0603f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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