名校
解题方法
1 . 已知数列
的前n项和为
,且满足
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,求证
.
![](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/212bcdba8a13e3aa7d8a2295ad9c4c50.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83de9a45d9b680da8835bac1fee9c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b692cace94f088567b07563ac71c46.png)
您最近一年使用:0次
2024-04-18更新
|
1284次组卷
|
2卷引用:北京市第九中学2023-2024学年高二下学期4月月考数学试卷
名校
解题方法
2 . 已知数列
中,
,
且
,其前
项和为
,且当
时,
.
(1)求证:数列
是等比数列;
(2)求数列
的通项公式;
(3)若
,令
,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/d47d50e2f34de24c9edf5f9a9279095f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.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/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b4870a2217cc3027f94946ffbd8860.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84474b4fab31b58ba1f449c5fb6066ff.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
3 . 已知数列
中,
, ,其中
.
从①数列
的前
项和
,②
,③
且
,这三个条件中一个,补充在上面的问题中并作答.
注:若选作多个条件分别解答,按第一个解答计分.
(1)求数列
的通项公式;
(2)设
,求证:数列
是等差数列;
(3)设数列
,求数列
的通项公式及前20项和 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff1e131c485875f292ab8b178d7fba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
从①数列
![](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/d5881af3b8af8ad275035969b325280b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b9c9864f294da867142cd20f273284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742dda3d3681ed568fdacde00e8ff11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a06d550b5258e4b9388f08347e3e4ff.png)
注:若选作多个条件分别解答,按第一个解答计分.
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb67957e82170c57e754bb5ccb45eda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
您最近一年使用:0次
解题方法
4 . 已知数列
满足
.
(1)求
的通项公式.
(2)若数列
的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19afd14e6a4af14fbbe3a3022a531d00.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f947547ff1ed0165a9a96cf196726e7.png)
您最近一年使用:0次
5 . 已知公差不为0的等差数列
满足
,且
成等比数列.
(1)求数列
的通项公式;
(2)设
,
为
的前
项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18556fda4a825861f1170cdeb059ff.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81c50676cbc29cfffdb62e15414c81c.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/6bad40ea8ed5619b07b43d4a037697dd.png)
您最近一年使用:0次
2022-07-10更新
|
631次组卷
|
2卷引用:北京市清华大学附属中学2021-2022学年高一下学期期末考试数学试题
11-12高三上·广东佛山·阶段练习
6 . 在等差数列
中,
,其前
项和为
,等比数列
的各项均为正数,
,公比为q,且
.
(1)求
与
;
(2)证明:
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c25b07f361e643922429bb4fe7b8c1f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a7ea33698be8ab4307379e647378c2.png)
您最近一年使用:0次
2022-06-17更新
|
475次组卷
|
16卷引用:2012届北京市高考模拟系列试卷(二)理科数学试卷
(已下线)2012届北京市高考模拟系列试卷(二)理科数学试卷【全国百强校】北京东城区北京二中2016-2017学年高一下学期期中考试数学试题(已下线)2012届广东省三水实验中学高三上学期第十次月考理科数学2016届宁夏六盘山高中高三上学期第二次月考理科数学试卷2015-2016学年重庆八中高二下第三次周考理科数学试卷2017届内蒙古杭锦后旗奋斗中学高三上入学摸底数学理试卷2017届山东寿光现代中学高三实验班10月月考数学(理)试卷四川省眉山市2016-2017学年高一下学期期末考试数学试题【全国百强校】甘肃省兰州第一中学2019届高三9月月考数学(文)试题江西省南康中学2018-2019学年高二下学期期中考试数学(理)试题智能测评与辅导[理]-算法 推理与证明陕西省西安市电子科技大学附属中学2019-2020学年高二上学期期中数学(理)试题海南省海口市灵山中学2020届上学期高三第三次月考试题广东省揭阳市普宁市华侨中学2021-2022学年高二下学期第三次月考数学试题(已下线)专题训练:数列综合运用大题-【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)四川省绵阳市三台中学校2021-2022学年高一下学期第四学月月考测试数学试题
7 . 已知等差数列
中,
.
(1)设
,求证:数列
是等比数列;
(2)求数列
的前
项和
.
(3)求数列
的前
项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c9bb109e5df8ce98f769724f7e5feb.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e191086446263b7bbbd93613577c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.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
8 . 设等差数列
的前
项和为
,
为各项均为正数的等比数列,且
,
,再从条件①:
;②:
;③:
这三个条件中选择一个作为已知,解答下列问题:
(1)求
和
的通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a916ef5c01b4391cca44b6d9a665ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4841a373b6c18a212534b2ea98516370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ff8ce3e59c069490084ffc200cfda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c230012c41291355e5443f18dbe9e264.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8243ce002108803cac56f03f39389176.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
2022-01-25更新
|
653次组卷
|
2卷引用:北京市通州区2021-2022学年高二上学期期末数学试题
9 . 已知数列
的前n项和为Sn,Sn+1=4an,n∈N*,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c79a9159d5c6453401c627057d2f254.png)
(1)证明:
是等比数列,并求
的通项公式;
(2)在①bn=an+1-an;②bn=log2
;③
,这三个条件中任选一个补充在下面横线上,并加以解答.已知数列{bn}满足_________,求{ bn }的前n项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c79a9159d5c6453401c627057d2f254.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dc43b8d11d5462e4b525dd7b03bcfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在①bn=an+1-an;②bn=log2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77288bfa684c2a9ca00c75743232a0e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbb8fed07e232b3960f61b4be1ff387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68eee81e090b96819b7df54fc1bcc3a6.png)
您最近一年使用:0次
2022-05-20更新
|
950次组卷
|
19卷引用:专题7.21 数列大题(结构不良型2)-2022届高三数学一轮复习精讲精练
(已下线)专题7.21 数列大题(结构不良型2)-2022届高三数学一轮复习精讲精练(已下线)江苏省七市(南通、泰州、扬州、徐州、淮安、连云港、宿迁)2021届高考三二模数学试题(已下线)必刷卷06-2021年高考数学考前信息必刷卷(江苏专用)(已下线)预测卷04-2021年高考数学金榜预测卷(山东、海南专用)湖北省华中师范大学第一附属中学2021届高三下学期四月综合测试数学试题广东省揭阳市普宁市华侨中学2021届高三下学期二模数学试题(已下线)专题2.4 数列-结构不良型-2021年高考数学解答题挑战满分专项训练(新高考地区专用)广东省梅江市梅州中学2022届高三上学期10月月考数学试题四川省资阳市高中2021-2022学年高三上学期第二次诊断性考试数学(理)试题(已下线)第2讲 数列通项与求和(讲·)-2022年高考数学二轮复习讲练测(新教材地区专用)江苏省盐城市2021-2022学年高二上学期期末数学试题1四川省资阳市2022届高三二诊数学理科试题2022届高三普通高等学校招生全国统一考试 数学预测卷(六)(已下线)期末测试卷02(B卷·提升能力)-2021-2022学年高二数学同步单元AB卷(苏教版2019选择性必修第一册)【学科网名师堂】湖北省襄阳市第五中学2022届高三下学期适应性考试(一)数学试题四川省泸县第一中学2022-2023学年高三上学期期末考试数学(文)试题四川省泸县第一中学2022-2023学年高三上学期期末考试数学(理)试题(已下线)期末测试卷01(基础卷)-【满分计划】2022-2023学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)第4章 数列(基础卷)-【满分计划】2022-2023学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)
2021·全国·模拟预测
10 . 在等差数列
中,
,其前n项和为
,各项均为正数的等比数列
中,
,且满足
,
.
(1)求数列
与
的通项公式;
(2)若数列
的前n项和为
,证明:
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968eb1910572edb648591d1dd90b53f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6661d6e240d8733d43b76172320854.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3860c78a8d25ac6b5c1cff5ebbd960fc.png)
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5卷引用:北京市一零一中学怀柔分校2022届高三高考数学模拟试题
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