1 . 等差数列
中,
,则数列
的公差![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67eaaaaee28891b63123ef9e5c6444c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
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名校
解题方法
2 . 已知正项数列
的前n项和为
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
______ .
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1e07c5b19e513d4155be61cd7e6798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
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3 . 已知
,删除数列
中所有能被2整除的数,剩下的数从小到大排成数列
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7196447bf70f4529d4e92fd442b5d5b7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be102b470b13adf5deb3540de8ea94e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7196447bf70f4529d4e92fd442b5d5b7.png)
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4 . 意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样的一列数:
,该数列的特点是:从第三个数起,每一个数都等于它前面两个数的和,人们把这样的一列数所组成的数列
称为“斐波那契数列”,则
是斐波那契数列中的第__________ 项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a638fcc8e7d8283654e836b24b938d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bda7bea727da80175e196a6041bbcb6.png)
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解题方法
5 . 设
是
的展开式中x项的系数(
),若
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b872f0cd4ac9a3c07b329cbcd5db0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52f28a846fe3f8365836f5fb69ed111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63412b2ecaac2889d95952cdc8930c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
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6 . 用
表示自然数
的所有因数中最大的那个奇数,例如:9的因数有
,
,10的因数有
,
,那么
=__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412c73872a41744bb74eebfba048d664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18c394cfe2aa1bef6baadf8703e03c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244cf53f0fcf787c289d0bd22aae75fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d991a3361309a8a006312748b129c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e3ddf574ba81dc32599ba356174c80.png)
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解题方法
7 . 数列
的项是由1或2构成,且首项为1,在第
个1和第
个1之间有
个2,即数列
为:1,2,1,2,2,2,1,2,2,2,2,2,1,…,记数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec6439c99c6a996a48b7d9e57c21208.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897d8f6cf00391f1b3ff70432f0121b4.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/dec6439c99c6a996a48b7d9e57c21208.png)
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8 . 数列
满足
,且对于任意的
都有
,则
等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ea12b5bf919a962f08bed2140d896b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2cbc577c3eb228535f96ceb298a205.png)
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9 . 用
表示自然数
的所有因数中较大的那个奇数,例如9的因数有1,3,9,则
;10的因数有1,2,5,10,则
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aab919d6b5a460956d0743318e29b1c.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e4bbad78eae5d4c694004f33b2ea52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d991a3361309a8a006312748b129c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aab919d6b5a460956d0743318e29b1c.png)
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2023-05-23更新
|
587次组卷
|
6卷引用:第十四届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
第十四届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)【全国百强校】辽宁省鞍山一中2019届高三(上)期中数学(理科)试题浙江省杭州市学军中学2017-2018学年高二下学期期中数学试题(已下线)第三篇 数列、排列与组合 专题1 建立递推关系求通项公式 微点1 建立递推关系求通项公式江西省萍乡市安源中学2022-2023学年高二下学期期中考试数学试题江苏省扬州中学2023届高三上学期11月月考数学试题
10 . 把正整数按一定的规则排成如图所示的三角形数表,设
(
)是位于这个三角形数表中从上往下数第
行,从左往右数第
个数,如
.若
,则
与
的和为__________ .
1
2 4
3 5 7
6 8 10 12
9 11 13 15 17
14 16 18 20 22 24
……
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0017117fab6f8e863c540552588e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43366cf92d2bbd350b6f2dcc9e14d712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2f9b53662f542a1c894c91b24a80cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
1
2 4
3 5 7
6 8 10 12
9 11 13 15 17
14 16 18 20 22 24
……
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