1 . 在严峻的疫情面前,为了响应教育部提出的“停课不停学”的政策,居家上网课已成为“宅家学生族”最熟悉的情景了.相较于在学校教室里线下课程而言,上网课少了课堂氛围,加上师生互动环节不惬意,学生听课缺乏专注力.鉴于此,为了提升同学们的听课效率,授课教师可以选择在授课过程中进行专注度监测,即要求同学们在10秒钟内在软件平台上按钮签到,若同学们能够在10秒钟内完成签到,则说明该同学在认真听课,否则就可以认为该同学目前走神了,经过一个月对全体同学上课情况的观察统计.平均每次专注度监测有90%的同学能够正常完成签到.为了能够进一步研究同学们上课的专注度情况,我们做如下两个约定:
①假设每名同学在专注度监测中出现走神情况的概率均相等;
②约定每次专注度监测中,每名同学完成签到加2分,未完成签到加1分.
请回答如下两个问题:
(1)若某班级共有50名学生,一节课老师会进行三次专注度监测,那么全班同学在三次专注度监测中的总得分的数学期望是多少?
(2)计某位同学在数次专注度监测中累计得分恰为
分的概率为
(比如:
表示累计得分为1分的概率,
表示累计得分为2的概率,
,试解决下列问题:
①求证:数列
为等比数列;
②求
的通项公式.
①假设每名同学在专注度监测中出现走神情况的概率均相等;
②约定每次专注度监测中,每名同学完成签到加2分,未完成签到加1分.
请回答如下两个问题:
(1)若某班级共有50名学生,一节课老师会进行三次专注度监测,那么全班同学在三次专注度监测中的总得分的数学期望是多少?
(2)计某位同学在数次专注度监测中累计得分恰为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e5134f738fa09b1c307fe7612a4022.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5a325806df1a1c3e7ce609fe99085f.png)
您最近一年使用:0次
2 . 已知
是各项均为正数的等比数列,公比为q,求证:
是等比数列,并求该数列的公比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c133f850a40f4d23c30fa91a1e7d74a2.png)
您最近一年使用:0次
2022-02-28更新
|
316次组卷
|
4卷引用:第4.3.1讲 等比数列的概念(第1课时)-2023-2024学年新高二数学同步精讲精练宝典(人教A版2019选修第二、三册)
(已下线)第4.3.1讲 等比数列的概念(第1课时)-2023-2024学年新高二数学同步精讲精练宝典(人教A版2019选修第二、三册)(已下线)4.3.2 等比数列的通项公式(已下线)4.3.1 等比数列的概念(精讲)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)苏教版(2019)选择性必修第一册课本习题 习题4.3(1)
3 . 判断下列数列是否为等比数列:
(1)9,0.9,0.09,0.009;
(2)
,
,
,
;
(3)
,
,
,
;
(4)
,
,
,
.
(1)9,0.9,0.09,0.009;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b57c4a905b766f8755d01b28d22a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993908fc9c1baaf8774ba080107c23d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd7d7624d5efbb189205bd3a4a13e3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bac900bd09df30926bbf18dcf94628a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5498db3231db49529b93fdf13433298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f5ca7640f5202cc27dd03190d101e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6e41b8e683c5d3b71c867b582524a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a9b9cada684621f0b080058a3582d3.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef25f1fa9539e95e763cd0ef4bf68782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b4d1868e26d04a2bd6b30a07d514c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3e49942ad60434e5ea393f722be9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425c4c772403a5d629255d864fe9abf4.png)
您最近一年使用:0次
4 . 已知数列
为等差数列,且
,
.
(1)求数列
的通项公式;
(2)令
,求证数列
为等比数列;
(3)令
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a84917c4f840f34385c1621a26e45fb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca857b7a6a1fe09827ecaa5f4c036069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7570419336e075b85fbad77e7160a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
5 . 定义函数
.数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bac366b967aa441db8fcd15381c8b35.png)
(1)若
,求
及
;
(2)若
且数列
为周期数列,且最小正周期
,求
的值;
(3)是否存在
,使得
成等比数列?若存在,求出所有这样的
,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e7313b65bbfb59ae13d3cad3c77dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8748938373768d7172dc2a8d43ee2d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bac366b967aa441db8fcd15381c8b35.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5dca4e85b2473ebe529b897e7c4086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7825eb57ef8a7f2021fa1859a914c4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da18ad56af5e38b1a5b73f44ba198fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2021-03-23更新
|
278次组卷
|
6卷引用:4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)2018年上海市南洋模范中学高考三模数学试题上海市嘉定区嘉定一中2021届高三上学期期中数学试题(已下线)4.3.1 等比数列的概念-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)(已下线)4.3.1-4.3.2 等比数列的概念和通项公式-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)4.3.1.2 等比数列的性质及应用(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)
名校
6 . 已知函数
的定义域为D,若存在实常数
及
,对任意
,当
且
时,都有
成立,则称函数
具有性质
.
(1)判断函数
是否具有性质
,并说明理由;
(2)若函数
具有性质
,求
及
应满足的条件;
(3)已知函数
不存在零点,当
时具有性质
(其中
,
),记
,求证:数列
为等比数列的充要条件是
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12ea6f9d2bbcc5a3d7980dbe79922d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c014d6dd9b1ba0c145f08767a6f522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c4c03f81039abf2fec0d1d504e7d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff8d1a032a46b55227a965e7616b5fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5079e2f37cefb15856bcaf754505cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d92fe568c519ab69cfe6088070ea17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78cac409e814b614cb060b6fc41caa85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389662f03137dce5ad957894ea7d6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808ef8edf6546fb634a902d50545aaed.png)
您最近一年使用:0次
2020-05-21更新
|
480次组卷
|
4卷引用:4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)2020届上海市松江区高三下学期模拟考质量监控数学试题上海市进才中学2021-2022学年高二下学期3月月考数学试题(已下线)4.3.1.2 等比数列的性质及应用(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)
名校
7 . 若数列
满足条件:存在正整数
,使得
对一切
,
都成立,则称数列
为
级等比数列;
(1)已知数列
为2级等比数列,且前四项分别为
、
、
、
,求
的值;
(2)若
(
为常数),且数列
是3级等比数列,求
所有可能的值,并求
取最小正值时数列
的前
项和
;
(3)证明:正数数列
为等比数列的充要条件是数列
既为2级等比数列,也为3级等比数列;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d285d7488e8d36ea8a48b16bf3baf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eecd38954cd0ca3fb26328a39bb859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8771e397fed0130b3f313e7cbc7a72de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61394ab3516811db7873f78179ef51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5e69a1736fce183c0227c991c14810.png)
(3)证明:正数数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
2020-01-07更新
|
653次组卷
|
5卷引用:4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)上海市松江二中2016-2017学年高三上学期第一次月考数学试题(已下线)专题02 过“三关”破解数列新情境问题 (第三篇)-2020高考数学压轴题命题区间探究与突破上海市七宝中学2021届高三冲刺模拟卷一数学试题(已下线)4.3.1.2 等比数列的性质及应用(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)
8 . 已知数列
的首项
,前
项和为
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa62ae5036e5a85b5fe37d348a2552d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214360ac0152818f5b95b805f6e615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2017-10-10更新
|
634次组卷
|
2卷引用:黑龙江省齐齐哈尔市第八中学校2023-2024学年高二下学期3月月考数学试题
9 . 已知数列
中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b760e2f0c2c2cdff85b8585df21084.png)
.
(1)是否存在实数
,使数列
是等比数列?若存在,求
的值;若不存在,请说明理由;
(2)若
是数列
的前
项和,求满足
的所有正整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b760e2f0c2c2cdff85b8585df21084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11c105ea15c7918ad68e86d12703639.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87515127a5f57b95f47ee18d27b96c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9403f1cbcbe70add5171ba9f0da996a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2016-12-03更新
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1018次组卷
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6卷引用:专题30 等比数列通项与前n项和
(已下线)专题30 等比数列通项与前n项和2015届江苏省苏州市高三上学期期末考试文科数学试卷(已下线)2015届江苏省苏州市高三上学期期末考试文科数学试卷【全国百强校】江苏省盐城中学2018届高三考前热身2数学试卷【全国百强校】江苏省海安高级中学2018-2019学年高二3月月考数学试题(已下线)专题29等比数列通项与前n项和-2022年(新高考)数学高频考点+重点题型