1 . 已知数列
满足
,
.
(1)证明:数列
为等比数列;
(2)在
与
之间插入
个数,使得这
个数组成公差为
的等差数列,求
.
![](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/57bfc1f8772f31748bfdc280d0712fc0.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4792fd59c4ca11ff03dc32e367c3983f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d1ae060458f733025fc82f7c7b14f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
名校
解题方法
2 . 已知
是各项均为正数的等差数列,其前
项和为
,满足
对任意的
成立.
(1)求
的通项公式;
(2)令
,记
为数列
的前
项和.证明:当
时,
.
![](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/6947966790678dcf4a1c6b9d30f556b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896c0ac826b417ab338050de7c837db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/45deada38f235bf0efb327bc4477034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12993f88db04326b694efa635fc1ef33.png)
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3 . 将数列
和
的公共项从小到大排列得到数列
,记
的前
项和为
.
(1)求
的通项公式;
(2)求使得
的
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3b236ce5ac46bf29625249180af284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a023e8c7e533834a3a00f6113eea60.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3f1f8813adcedd56b471961b2ad6a6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade47598510917b18557339027024b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4 . 已知数列
满足
.
(1)记
,写出
,并求数列
的通项公式;
(2)求
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea64f717c0551fa1715379f2dc0f233.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314501f06c7e4bf3112fe41ecac7be68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bc85af36f64be115dd7c5d88fac6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
5 . 记
为数列
的前n项和,
是首项与公差均为1的等差数列.
(1)求数列
的通项公式;
(2)设
,求数列
的前2024项的和
.
![](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/96ba2b14e2a43f387d78a33e77813f2a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0e1f31866a3fbfb90d92044202bcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
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名校
解题方法
6 . 已知等比数列
的前
项和为
,且
.
(1)求数列
的通项公式.
(2)在
与
之间插入
个数,使这
个数组成一个公差为
的等差数列,求
及其最小值.
![](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/28d86858313c2f80b83aef22fc48d977.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
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解题方法
7 . 已知数列
的前
项和为
,且
满足
.
(1)求数列
的通项公式;
(2)数列
的通项
,求
的前
项和
;
(3)在任意相邻两项
与
(其中
)之间插入
个3,使它们和原数列的项构成一个新的数列
.记
为数列
的前
项和,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21bdc437e0e1c6e176adc70099d5f84.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](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/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(3)在任意相邻两项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98aa5f1acb67ec4580d240c2525e4d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6468d06ec9604a25a15ff3ca790c67.png)
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解题方法
8 . 已知等差数列
的前
项和为
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156ff12ebc86677c4215a8f0563ef4ed.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.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
今日更新
|
816次组卷
|
4卷引用:河北省深州中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
9 . 已知数列
是公比为
的正项等比数列,且
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e15be6eb86b5f1746b0036a87c9ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb6ae18e9f28cbefd073bd6ac0c9e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d787262919c1d297882486899b8f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58117e8491e2af9216622235f2671b5f.png)
A.4050 | B.2025 | C.4052 | D.2026 |
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372次组卷
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3卷引用:辽宁省大连市第二十四中学2023-2024学年高二下学期期中考试数学试卷
辽宁省大连市第二十四中学2023-2024学年高二下学期期中考试数学试卷(已下线)专题07 数列通项公式与数列求和--高二期末考点大串讲(人教B版2019选择性必修第三册)青海省西宁市第十四中学2023-2024学年高二下学期6月月考数学试卷
名校
解题方法
10 . 若“
,
”为真命题,则实数a的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c501353a892ca1eec0594c53e6b743ed.png)
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