1 . 一个弹性小球从30米高处自由落下,每次着地后反弹到原来高度的
处,再自由落下,若这个小球能无限次反弹,则这个小球经过的总路程为________ 米
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
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2 . 某集团投资一工厂,第一年年初投入资金5000万元作为初始资金,工厂每年的生产经营能使资金在年初的基础上增长50%.每年年底,工厂向集团上缴
万元,并将剩余资金全部作为下一年的初始资金,设第n年的初始资金为
万元.
(1)判断
是否为等比数列?并说明理由;
(2)若工厂某年的资金不足以上缴集团的费用,则工厂在这一年转型升级.设
,则该工厂在第几年转型升级?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93a232c88870d213a7b74a796a1ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8be23e4b772df85968e9a0afde88815.png)
(2)若工厂某年的资金不足以上缴集团的费用,则工厂在这一年转型升级.设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c999cfa4c0e1507032047eabaa56ceed.png)
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3 . 正项等比数列
中,
与
是
的两个极值点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972a067d9d035b9be7768a2e23dee986.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e29f6ffe091d4f51b3b7c8c9ca88005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74fd9b94d7e7c54207580a3823b381a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972a067d9d035b9be7768a2e23dee986.png)
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4 . 在公差为正数的等差数列
中,若
,
,
,
成等比数列,则数列
的前10项和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a9d83c51e4c25b71bbb8a15de4e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024-05-14更新
|
650次组卷
|
3卷引用:上海市民办南模中学2023-2024学年高一下学期期末考试数学试卷
名校
5 . 设
是公比不为1的无穷等比数列,则“
为严格减数列”是“存在正整数
,当
时,
”的______ 条件.(选填“充分而不必要条件”,“必要而不充分条件”,“充分必要条件”,“既不充分也不必要条件”)
![](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/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25809c4ad8f07e80b10fdb5b40d6dfae.png)
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6 . 已知数列
的前
项和为
,若
(
是正整数),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.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/34c57356fade5a5d8e46c4750ac4bb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
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2024-05-08更新
|
976次组卷
|
4卷引用:上海市徐汇区2024届高三学习能力诊断数学试卷
上海市徐汇区2024届高三学习能力诊断数学试卷(已下线)模块3 专题1 第4套 小题进阶提升练【高二人教B】(已下线)5.1 数列的概念及其表示(高考真题素材之十年高考)安徽省六安市金寨县青山中学2023-2024学年高二下学期期中考试数学试题
解题方法
7 . 数列
中,
是其前
项的和,若对任意正整数
,总存在正整数
,使得
,则称数列
为“某数列”
现有如下两个命题:①等比数列
为“某数列”;②对任意的等差数列
,总存在两个“某数列”
和
,使得
.则下列选项中正确的是( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3693c7c942afef5517a3c18997c878df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a97e99f49ad1998d2858e1963aa45de.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6076227a7a825358aeb27b5633613a2c.png)
A.①为真命题,②为真命题 | B.①为真命题,②为假命题 |
C.①为假命题,②为真命题 | D.①为假命题,②为假命题 |
您最近一年使用:0次
8 . 数列
中的项按顺序可以排列成如下图的形式,第一行一项,排
;第二行2项,从左到右分别排
,
;第三行3项,…依次类推,设数列
的前
项和为
,则满足
的最小正整数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.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/38f2c173004bcd025e5d4759fa14faa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
4 | |||
4 | ![]() | ||
4 | ![]() | ![]() | |
4 | ![]() | ![]() | ![]() |
…… |
A.65 | B.66 | C.78 | D.79 |
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解题方法
9 . 设
,
,
是正整数,
是数列
的前
项和,
,
,若
,且
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b3a76992503393f74712a724e3a0cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae30f0e425814c6b7005e46d65949a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7877dccf462e5eb837589fa3ed8a360f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dfa88dd2410bf39672ab47040ba8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
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解题方法
10 . 已知数列
的前
项和
满足,对任意的
,
,
成立,求:
的值
![](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/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711161d23bed5161de370857a687c3ea.png)
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