1 . 已知数列
的前
项和为
,且
是首项为1,公差为2的等差数列.
(1)求
的通项公式;
(2)若数列
的前
项和为
,且不等式
对一切
恒成立,求实数
的取值范围.
![](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/c51f1c6ae196c2564d23a620d2cded7a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4438efb49eee52ca57c9130fef7ebbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-01-03更新
|
1053次组卷
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5卷引用:海南省海口市海南中学2023-2024学年高二上学期期末考试数学试题
名校
2 . 某果园种植了甲、乙两种蜜桔品种,为给该果园制定蜜桔销售计划,对蜜桔产量进行了预估,从甲、乙两种蜜桔中分别采摘了
个进行单个称重,其质量(单位:克)分布在区间
,
,
,
,
上,并将数据进行汇总整理,得到甲、乙两种蜜桔质量的频率分布直方图如图所示
同一组数据用该区间的中点值作代表
.
(2)视频率为概率,已知该果园乙种蜜桔树上大约有
万个蜜桔等待出售,某水果批发商提出了两种收购方案:
方案一:所有蜜桔均以
元
千克收购;
方案二:质量适中的蜜桔深受消费者青睐,该批发商建议低于
克的蜜桔以
元
千克收购,不低于
克的蜜桔以
元
千克收购,其他蜜桔以
元
千克收购.
请你通过计算判断哪种收购方案能使该果园收益最大.
(3)现采用不放回抽取的方法从甲种蜜桔中随机逐个抽取,直到抽到的蜜桔的质量在区间
内或抽取了
个为止,设抽取的蜜桔个数为
,求随机变量
的数学期望(结果精确到个位).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0711b72603ec671b07f099377e74f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762aed7532094dfc87709c4b3b4fd2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652b8aa0cb0bdce1d8e7ba8304849778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3cd26075fea64e935d0e05ad8f6781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fc138be9688253cbdeae2808eb74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)视频率为概率,已知该果园乙种蜜桔树上大约有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
方案一:所有蜜桔均以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
方案二:质量适中的蜜桔深受消费者青睐,该批发商建议低于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
请你通过计算判断哪种收购方案能使该果园收益最大.
(3)现采用不放回抽取的方法从甲种蜜桔中随机逐个抽取,直到抽到的蜜桔的质量在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762aed7532094dfc87709c4b3b4fd2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的前
项和
满足:
.
(1)求
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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e1bc2e9bf38da862b2cf0dbef14aa0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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
2022-10-16更新
|
1950次组卷
|
5卷引用:海南省琼海市嘉积中学2022-2023学年高二上学期期末数学试题
海南省琼海市嘉积中学2022-2023学年高二上学期期末数学试题(已下线)期末押题预测卷(提升卷)(考试范围:选择性必修第一册)-【单元测试】2022-2023学年高二数学分层训练AB卷(苏教版2019选择性必修第一册)重庆市璧山来凤中学校2023届高三上学期10月月考数学试题陕西省西安市周至县第四中学2022-2023学年高三上学期期中文科数学试题湖南省长沙市第一中学2022-2023学年高三上学期月考(四)数学试题
解题方法
4 . 已知数列
的前
项和
,且
.
(1)证明:数列
为等差数列;
(2)设
,记数列
的前
项和为
,若
,对任意
恒成立,求实数
的取值范围.
![](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/38bc0c25fb22d1a1965fe854b487dee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d3c671f373f48752d9125c2797b066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
为各项均为正数的等比数列,且
,
.
(1)求数列
的通项公式;
(2)令
,求数列
前n项和
.
![](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/32f4820363fce8bd3cc21a95e787c3de.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc1f3466622a3a27a7b6013e7748b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-12-23更新
|
2342次组卷
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7卷引用:海南省华东师范大学第二附属中学乐东黄流中学2022-2023学年高二上学期12月教学质量监测(期末)数学试题
(已下线)海南省华东师范大学第二附属中学乐东黄流中学2022-2023学年高二上学期12月教学质量监测(期末)数学试题福建省福州市协作体四校2021-2022学年高二上学期期末联考数学试题湖南省岳阳县第一中学、汨罗市第一中学2022-2023学年高二上学期期末考试数学试题湖南省永州市第一中学2021-2022学年高二上学期期末模拟数学试题黑龙江省哈尔滨市第三十二中学校2021-2022学年高三上学期期中考试文科数学试题(已下线)2020年高考全国3数学理高考真题变式题16-20题(已下线)2020年高考全国1数学理高考真题变式题16-20题
解题方法
6 . 已知
是递增的等比数列,
是方程
的根.
(I)求
的通项公式;
(II)求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14877bf6d7297f02feff3468abf01f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bc85419a13c4edb085384e84bcb556.png)
(I)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(II)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da48cb02b05c93e2e4091e868e32f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
7 . 已知数列
是单调递增的等比数列,且各项均为正数,其前
项和为
,
,
,
,
成等差数列.
(1)求数列
的通项公式;
(2)若______,求
的前
项和
,并求
的最小值.
从以下所给的三个条件中任选一个,补充到上面问题的横线上,并解答此问题.
①数列
满足:
,
(
);
②数列
的前
项和
(
);
③数列
的前
项和
满足:
(
).
注:如果选择多个条件分别解答,只按第一个解答计分.
![](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/7c2b0c69e8ade46efb5228a9bd3f5575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b12e24df620bb5a46cdcbc236061fe3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若______,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
![](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/bf83e20035c3afd6d26ebfd53d768a70.png)
从以下所给的三个条件中任选一个,补充到上面问题的横线上,并解答此问题.
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332cbbc3ad16e694a259948882db19d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104a7517cf0b4328a13925eafce0c9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
③数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6109a756aa026d90c0181f1b578b37d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
注:如果选择多个条件分别解答,只按第一个解答计分.
您最近一年使用:0次
2020-12-20更新
|
1347次组卷
|
5卷引用:海南省海口市海南中学2023-2024学年高二上学期期末数学模拟试题
海南省海口市海南中学2023-2024学年高二上学期期末数学模拟试题山东省淄博市2021届高三上学期教学质量摸底检测(零模)数学试题(已下线)2021届高三高考数学适应性测试八省联考考后仿真系列卷十重庆市江津中学、铜梁中学、长寿中学等七校联盟2021届高三三模数学试题(已下线)第20讲 数列的通项公式-2022年新高考数学二轮专题突破精练
解题方法
8 . 已知数列
的前n项和为
,
.
(1)求
;
(2)若
,求数列
的前n项和
.
![](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/b530b6a38de32263a84684445d4fc609.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ae14c59e337f6ce91f55a040c040eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2020-12-03更新
|
1249次组卷
|
5卷引用:海南省儋州市2023-2024学年高二下学期期末考试数学试题
海南省儋州市2023-2024学年高二下学期期末考试数学试题广东省肇庆市2021届高三一模数学试题(已下线)黄金卷16-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)(已下线)重组卷01-冲刺2021年高考数学之精选真题+模拟重组卷(新高考地区专用)广东省佛山市南海区南海艺术高级中学2022届高三下学期第四次综合测试数学试题
名校
9 . 设等比数列
的前
项和为
,已知
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)令
,设数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b000a7c2c4f29d089bbd1445aa56d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d3082535753c0bc409f739d99d5b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207f8611762e9260b419fc95bed2e4b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab67487086fb731b607dbda229b3caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2019-02-01更新
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493次组卷
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2卷引用:【区级联考】海南省海口市龙华区2018-2019学年高二第一学期期末学业质量监测试卷数学(文)试题
10 . 已知数列
的前
项和
,数列
满足
,
,
(Ⅰ)求数列
和数列
的通项
和
;
(Ⅱ)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d255ea8e125b603d6b640bdf4a804922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcba622ae8d5e614f5f59982ce9b9b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a161b12ac9ba38aa73f386242908bed1.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b57fc61aae0064542bbb65f1df944a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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