1 . “现代五项”是由现代奥林匹克之父顾拜旦先生创立的运动项目,包含射击、击剑、游泳、马术和越野跑五项运动.已知甲、乙、丙共三人参加“现代五项”.规定每一项运动的前三名得分都分别为
,
,
(
且
),选手最终得分为各项得分之和.已知甲最终得22分,乙和丙最终各得9分,且乙的马术比赛获得了第一名,则游泳比赛的第三名是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17b39cf99251d5f357317f531acf25a.png)
A.甲 | B.乙 | C.丙 | D.乙和丙都有可能 |
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2 . 两千多年前,古希腊毕达哥拉斯学派的数学家曾经在沙滩上研究数学问题,他们在沙滩上画点或用小石子来表示数,按照点或小石子能排列的形状对数进行分类,如图中的实心点个数1,5,12,22,…,被称为五角形数,其中第1个五角形数记作
,第2个五角形数记作
,第3个五角形数记作
,第4个五角形数记作
,…,若按此规律继续下去,得到数列
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
___________ ;对
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0939caf47d751f8c7139bd0b25fe98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5202b28df649fd77f8fa2891e8d36322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/c5938698-bbc2-4615-a41f-cb1ad7f2e22e.png?resizew=296)
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3 . 将全体正奇数排成一个三角形数阵:
1
3 5
11 9 7
13 15 17 19
29 27 25 23 21
. . . . . . . . .
按照以上排列的规律,前n行(n ≥3)下列结论正确的是( )
1
3 5
11 9 7
13 15 17 19
29 27 25 23 21
. . . . . . . . .
按照以上排列的规律,前n行(n ≥3)下列结论正确的是( )
A.若n是偶数,第n 行从左向右的第3 个数是 ![]() |
B.若n是奇数,第n 行从左向右的第3 个数是 ![]() |
C.若n是奇数,第n 行从左向右的第3 个数是 ![]() |
D.前n 行所有数的和是![]() |
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4 . 设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
,将
个数
依次放入编号为1,2,…,
的
个位置,得到排列
.将该排列中分别位于奇数与偶数位置的数取出,并按原顺序依次放入对应的前
和后
个位置,得到排列
,将此操作称为C变换,将
分成两段,每段
个数,并对每段作C变换,得到
;当
时,将
分成
段,每段
个数,并对每段C变换,得到
,例如,当
=8时,
,此时
位于
中的第4个位置.
(1)当
=16时,
位于
中的第___ 个位置;
(2)当
(
)时,
位于
中的第___ 个位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e84c08aba58d7695d39e6b4f85acb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f1d912a8e5adc6eb21b301ba7e85b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2a9a08064daadeea0f1acd731053fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f042ab7f9e19baf5cc3c3d605ba9bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabdfa40d74bc127ed1e478b4a253c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fe33ffb69050c0627f8eaba1131fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24879b60db93a877f50cdbd8edf557d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab53ffd5d6034c1722c2502e5d8f2ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb0c78fec78916bbbfca7cc2a4da3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e382c9bafdc5d09498b92f5248d01c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e382c9bafdc5d09498b92f5248d01c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efe6197f4849aca8059c0a9bbf5225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322ba729eb66e803e13fc1dc6f37d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c438eee3096c6eb60d87c2c98c7c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
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