1 . 已知数列
是正项等比数列,且
,
,若数列
满足
,
.
(1)求数列
和
的通项公式;
(2)已知
,记
.若
恒成立,求实数t的取值范围.
![](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/c94c038344552b799dc53e6bce1b245f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f732837af71ad315d4f7cb7a155eb8e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bbb4dd887b78810c2bffdbbaae1559.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cbcd64777f0a23fd80d8422e51b419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b667de0002d5ebc53b9d9c804d30d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8bd231428639727d3c8d0d1c219b30.png)
您最近一年使用:0次
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|
1606次组卷
|
5卷引用:辽宁省五校2022-2023学年高二下学期期末数学试题
名校
2 . 在等比数列
中,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329785900390130a04a57d0b55aaa569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8808baa172a4b4201f1a2c05a03bb4ce.png)
A.8 | B.6 | C.4 | D.3 |
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3卷引用:辽宁省沈阳市级重点高中联合体2022-2023学年高二下学期期中数学试题
名校
解题方法
3 . 在递增等比数列
中,其前
项和为
,且
是
和
的等差中项,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/aa8bed9dea293924486b60a926c8ec6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce44cdc798888e0920e0441deadd255.png)
A.28 | B.20 | C.18 | D.12 |
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9卷引用:辽宁省农村重点高中协作校2023届高三第三次模拟考试数学试题
4 . 已知
,若
.
(1)求数列
通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c177a84021ea8232da7dc84c98fb017a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beba4197fd2f0d864f9a5f03a2c81b46.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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2024-01-31更新
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2卷引用:辽宁省抚顺市抚顺县高级中学校2023-2024学年高二下学期第一次教学质量检测数学试卷
5 . 已知数列
满足
,
.
(1)证明:数列
是等比数列;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510fdcb4d1398c334fa619f1dd87b6ba.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec783bca4d43c17bfbad1bb85b094f6a.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/08eb71ecf8d733b6932f4680874dbbf3.png)
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2023-11-15更新
|
1319次组卷
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3卷引用:辽宁部分学校2023-2024学年高三上学期期中大联考数学试题
名校
解题方法
6 . 如图,已知曲线
及曲线
.从
上的点
作直线平行于
轴,交曲线
于点
,再从点
作直线平行于
轴,交曲线
于点
,点
的横坐标构成数列
.
与
之间的关系,并证明:
;
(2)若
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af82160c02868bb45fc65d7597c84027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39da03b091bb40dd965458631bf50786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0fb5c4c19ac84d269620933529d592d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76717a33aa190b392c6a3badea1aaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cd245dba055034203e2450ba9b8848.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2023-05-23更新
|
1522次组卷
|
9卷引用:辽宁省沈阳市浑南区东北育才学校科学高中部2023-2024学年高三上学期高考适应性测试(一)数学试题
辽宁省沈阳市浑南区东北育才学校科学高中部2023-2024学年高三上学期高考适应性测试(一)数学试题湖南师范大学附属中学2023届高三一模数学试题专题13数列(解答题)(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2 建立递推关系求通项公式综合训练(已下线)第五章 数 列 专题1 数列中的不等关系的证明(已下线)第五章 数列 专题1 数列中的不等关系的证明(已下线)第04讲 数列的通项公式(十六大题型)(讲义)-4(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2(已下线)压轴题05数列压轴题15题型汇总-3
7 . 已知
是首项为1的等比数列,
是首项为2的等差数列,
且
.
(1)求
和
的通项公式;
(2)将
和
中的所有项按从小到大的顺序排列组成新数列
,求数列
的前50项和
;
(3)设数列
的通项公式为
,
,记
的前
项和为
,若
对任意的
都成立,求正数
的取值范围.
![](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/a4ccd62deec96fa702562bb4fbb797ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0634b9b4a6716bb7dae3aff7d6d2630.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)将
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a901aa78366ac960f5f4e7f1fcbac.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34ca593d2c68fbe9bdcf0ffd2a7f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.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/04f8bc7db6652ad666daf9a97fa15f04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-01-13更新
|
1446次组卷
|
3卷引用:辽宁省沈阳二中2023-2024学年高二下学期第一次阶段测试数学试题
名校
解题方法
8 . 记
为数列
的前
项和,已知
.
(1)求
的通项公式;
(2)设单调递增的等差数列
满足
,且
成等比数列.
(i)求
的通项公式;
(ii)设
,证明:
.
![](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/b9aa8c8737223748f099a5c437f3a2cb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设单调递增的等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975a03319e38805eb6e5baa4febe03a4.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ac70d32577ec72558ed5010069c32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
您最近一年使用:0次
2023-06-05更新
|
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3卷引用:辽宁省锦州市2023届高三质量监测数学试题(最后一模)
名校
9 . 四个实数,2,x,y按照一定顺序可以构成等比数列,则xy的可能取值有( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-05更新
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1319次组卷
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4卷引用:辽宁省大连市第一中学2024届高三上学期11月阶段性学情反馈数学试题
10 . “杨辉三角”是二项式系数在三角形中的一种几何排列.从第
行开始,第
行从左至右的数字之和记为
,如
,
,
,
的前
项和记为
,依次去掉每一行中所有的
构成的新数列
、
、
、
、
、
、
、
、
、
、
,记为
,
的前
项和记为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38eec2adafdf745ca8ad514469549abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7df0430db8db9fc354ffdd038fb432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c996a43ff8843aec0be0a9d0ac0e9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/38eec2adafdf745ca8ad514469549abb.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.![]() |
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