名校
解题方法
1 . 在数列
中,
,且对任意
,
,
,
成等差数列,其公差为
.
(1)若对任意
,
,
,
成等比数列,其公比为
.设
,证明:
是等差数列;
(2)若
,证明:
,
,
成等比数列(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b6ecfdff9d2b29ef64d2a6f3343f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069c88b849f37a1597cb7e9cdcb1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904e7018ec79c8b0efdcb3ba67cb7cb.png)
(1)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069c88b849f37a1597cb7e9cdcb1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952162dafce99cb22b05a1e313df53ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9778f679a2495d92a52b36e5e86d4b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1e7059a9d5555935ffded7be5f8c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1490fc8c90d79ab85d83f98667e177.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597f7f45c16b0f1f35acbb4528863311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069c88b849f37a1597cb7e9cdcb1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952162dafce99cb22b05a1e313df53ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
您最近一年使用:0次
名校
2 . 已知等比数列
的前n项和为
,
,且-3,
,
成等差数列,则数列
的通项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.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/3d583b2cc49292ba3497b6d3e4abd807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b14f57fc31a04b24a84d1e114fbb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次
2023-10-10更新
|
902次组卷
|
4卷引用:河北省石家庄市新乐市第一中学2024届高三上学期10月月考数学试题
河北省石家庄市新乐市第一中学2024届高三上学期10月月考数学试题甘肃省兰州市第一中学2023-2024学年高二上学期10月月考数学试题(已下线)专题08 数列(5大易错点分析+解题模板+举一反三+易错题通关)(已下线)4.3等比数列(4)
名校
解题方法
3 . 记
为公比不是1的等比数列
的前n项和.设甲:
,
,
依次成等差数列.乙:
,
,
依次成等差数列.
.则( )
![](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/357c8144569e482df835ea46b73e5602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c0f8f84ee314c1853a758f73cfda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9827971dc80f4038c7fee608ea1886c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacf94481a81f2c7e071bb46ae2a91f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fea3a3863895248228fefdba728edb3.png)
A.甲是乙的充分条件但不是必要条件 |
B.甲是乙的必要条件但不是充分条件 |
C.甲是乙的充要条件 |
D.甲既不是乙的充分条件也不是乙的必要条件 |
您最近一年使用:0次
2023-10-10更新
|
506次组卷
|
2卷引用:浙江省新阵地教育联盟2024届高三上学期第二次联考数学试题
解题方法
4 . 已知数列
的前n项和为
,且满足
.
(1)求数列
的通项公式;
(2)已知
,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/cba0b54f0504b2946b615dd96f10bd71.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582df36348994ad4202356151d06c305.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
5 . 设等差数列
的前
项和为
,公差为
,且
,若等差数列
满足
.
(1)求
的通项公式;
(2)若
,记数列
的前
项和为
,且
,求
的最小值.
![](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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e41b0ba53890b1c939a38f6ca5f466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911c88654ea7669c5e54542b0f16d89a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25e2d969c2aae6614c1b702f0cfe514.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/81452025a089e84e5de3f3d321da32bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
6 . 公差不为零的等差数列
的前为
项和为
,若
,则
( )
![](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/f02ffa2864b1fbf4cf24c48d77305d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.8 | B.12 | C.16 | D.9 |
您最近一年使用:0次
7 . 已知椭圆C:
的左右焦点为
,过
的直线与
交于
两点,若满足
成等差数列,且
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119a89432a10a7430a63b32f37ef0365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7d3219e2373204fb4d2de42e5deef4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 记
为等比数列
的前
项和,且
成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c78886c192480eb5dec0ee3c61b23f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1876f2bf6ef89c0684f95f6d07e04f70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36243198e5e20c56399e4ad5ac3c519.png)
A.126 | B.128 | C.254 | D.256 |
您最近一年使用:0次
2023-10-03更新
|
850次组卷
|
8卷引用:河北省衡水市衡水中学2024届高三上学期四调考试数学试题
河北省衡水市衡水中学2024届高三上学期四调考试数学试题福建省宁德市福鼎市第一中学2023-2024学年高二上学期10月月考数学试题河北省部分高中2024届高三上学期12月期末数学试题(已下线)第4章 数列综合能力测试-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)重庆市九龙坡区八中科学城中学校2023-2024学年高二(艺术班)上学期期末数学试题重庆市第八中学校2023-2024学年高二艺术班上学期期末数学试题(已下线)4.3等比数列(4)(已下线)专题4.3 等比数列(5个考点八大题型)(3)
名校
解题方法
9 . 已知数列
是公比
的等比数列,前三项和为39,且
成等差数列.
(1)求数列
的通项公式;
(2)设
,求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944a9c2574548d3305c0d55a58206f34.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce013e23c18e8e496a19cfa7e0ad46a4.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
2023-09-21更新
|
2582次组卷
|
5卷引用:吉林省长春市第二实验中学2023-2024学年高三上学期9月月考数学试题
吉林省长春市第二实验中学2023-2024学年高三上学期9月月考数学试题福建省厦门市湖滨中学2024届高三上学期10月月考数学考试题湖南省永州市2024届高三一模数学试题(已下线)专题01 数列大题(已下线)第08讲 第四章 数列 重点题型章末总结-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)
名校
10 . 数学兴趣小组对具有线性相关的两个变量x和y进行了统计分析,得到了下表:
x | 4 | 6 | 8 | 10 | 12 |
y | a | 2 | b | c | 6 |
并由表中数据求得y关于x的回归方程为,若a,b,c成等差数列,则
您最近一年使用:0次
2023-09-19更新
|
767次组卷
|
9卷引用:黑龙江省牡丹江市第三高级中学2024届高三上学期第三次月考数学试题
黑龙江省牡丹江市第三高级中学2024届高三上学期第三次月考数学试题陕西省西安市第八十三中学等校2023届高三二轮复习联考(一)文科数学试题(已下线)第三节 成对数据的统计分析(第一课时) B卷素养养成卷 一轮复习点点通山东省潍坊市实验中学2024届高三上学期12月周测数学试题(已下线)考点16 回归模型 2024届高考数学考点总动员(已下线)专题04 回归分析与独立性检验的应用(四大类型)8.2.1一元线性回归模型练习(已下线)第八章 成对数据的统计分析(单元重点综合测试)(19题新结构)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第三册)(已下线)第八章 成对数据的统计分析(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)