名校
解题方法
1 . 已知数列
是递增的等差数列,
是各项均为正数的等比数列
,
,
,
.
(1)求数列
和
的通项公式;
(2)设
,求数列
的前9项的和
.
(注:
表示不超过x的最大整数)
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f1d6bb8ddc8852af39c269b6957e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a448133261808dc7f564d15995fd9ffd.png)
(1)求数列
![](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/2b6752e8599eb1a562212a0ffd2a2ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff530320a228db7b1a3639f925013ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
(注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
您最近一年使用:0次
2022-05-13更新
|
881次组卷
|
3卷引用:江苏省连云港市2022届高三下学期高考前模拟(一)数学试题
名校
解题方法
2 . 设
为等差数列
的前n项和,且
,
.
(1)求数列
的通项公式;
(2)若
,求数列
的前30项和
.
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e17b3a240d38a30f9575f447184cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f550f4135c46fbfb0c001e662cd8ff6.png)
您最近一年使用:0次
2022-05-12更新
|
1018次组卷
|
5卷引用:江苏省徐州市第七中学2022届高三下学期高考前模拟一数学试题
3 . 记数列{
}的前n项和为
.已知
,___________.
从①
;②
;③
中选出一个能确定{
}的条件,
补充到上面横线处,并解答下面的问题.
(1)求{
}的通项公式:
(2)求数列{
}的前20项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8c4060c7a614a2f287e9fa8fd9f627.png)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31148cf610ce41888d79538d1dafcb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842b9a65ee998c6fa24ab651d90a9ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b3d3b1e4633d3f7da681788346c3be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
补充到上面横线处,并解答下面的问题.
(1)求{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde4c9452a81d3adc834c4c9bc53b73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f710b0e6ccca316852bf3a94f68135.png)
您最近一年使用:0次
2022-05-11更新
|
1550次组卷
|
4卷引用:江苏省淮安市2022届高三下学期5月模拟数学试题
名校
解题方法
4 . 在①
,
;②
,
;③
,
三个条件中选择合适的一个,补充在下面的横线上,并加以解答.已知
是等差数列
的前
项和,
,数列
是公比大于1的等比数列,且_____.
(1)求数列
和
的通项公式;
(2)记
,求使
取得最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fa50a0797b57c697d06c3143d999f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bdb8aaf564b8e84435e382a9109ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90221b91dabf8a382486cdb4fea5d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a738600092c6dbff35a59954f8b0788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a539f4656a7ff726f3cd77321bd92744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e46afd640072fd6a5e2c94bb72c698b.png)
![](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/4414e88541187aa93beb4b5c2601862c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbf68dfbe8feafc4d6b9218b352ffee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-05-05更新
|
1503次组卷
|
3卷引用:江苏省苏锡常镇四市2022届高三下学期5月教学情况调研(二)数学试题
名校
解题方法
5 . 已知数列
的前n项积为
,且满足a1=1,
.
(1)求
的通项公式;
(2)若数列
满足
,证明:
=
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaaf99eccaf6d531684dcd60e71670aa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0626b7c7e4ee8596fb01fe93cea17bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ceba3c178fc9ce05e3d449dcb644381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10eec31086b34ab9d2eecf7547b8a119.png)
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2022-09-14更新
|
480次组卷
|
3卷引用:江苏省2023届高三上学期起航调研测试(Ⅱ)数学试题
名校
解题方法
6 . 已知数列
的前n项和为
,若
,
.
(1)求证:数列
是等差数列;
(2)从下面两个条件中选一个,求数列
的前n项的和
.
①
;
②
.
![](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/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83faef830e461f4772b0f335a9a6daf.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)从下面两个条件中选一个,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939366f52d33ae3f69b101251eaa02da.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7c2b537a8f47ad2a8bef4d9895d227.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22e9ccd690ac8027b3b8205ed467d56.png)
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2022-04-24更新
|
1110次组卷
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6卷引用:江苏省扬州市高邮市第一中学2022届高三下学期二模适应性考试数学试卷
江苏省扬州市高邮市第一中学2022届高三下学期二模适应性考试数学试卷山西省2022届高三第二次模拟数学(理)试题黑龙江省大庆实验中学2021-2022学年高考数学预测试题(二)理工类试题山西省朔州怀仁市2022届高三第三次模拟数学(理)试题(已下线)考点14 等差数列与等比数列(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)第08讲 等差、等比数列- 1
7 . 已知数列
前n项积为
,且
.
(1)求证:数列
为等差数列;
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c0821e7d0410e8a5adb7fd4070a52c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d376c42ae1c68747af6df554b1c4a99e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf48cd99db12af9a0652d37ffbbd348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dfa46a983634a7c520e495b805d324.png)
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2022-04-23更新
|
4306次组卷
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15卷引用:江苏省南通市海安市2022届高三下学期4月阶段检测(2.5模)数学试题
江苏省南通市海安市2022届高三下学期4月阶段检测(2.5模)数学试题江苏省南通市海安高级中学2022届高三下学期4月阶段性检测(二模)数学试题(已下线)押新高考第18题 数列-备战2022年高考数学临考题号押题(新高考专用)(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用) (5月30日)(已下线)2022年高考考前20天终极冲刺攻略(二)【理科数学】(已下线)考点13 数列概念及通项公式(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)考点14 等差数列与等比数列(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)专题26 数列的通项公式-4(已下线)第08讲 等差、等比数列- 1(已下线)第6讲 数列的通项公式的11种题型总结(4)(已下线)第7讲 数列求和9种常见题型总结 (3)辽宁省沈阳市皇姑区2023届高三上学期期中数学试题(已下线) 第4章 数列单元测试基础卷-2023-2024学年高二数学上学期人教A版(2019)选择性必修第二册湖北省武汉市华中师大第一附中2023-2024学年高二上学期期末模拟数学试题(已下线)微考点4-2 新高考新试卷结构数列的通项公式的9种题型总结
名校
解题方法
8 . 已知数列
是公差不为零的等差数列,
是各项均为正数的等比数列,
.
(1)求数列
和
的通项公式;
(2)设
,求数列
的前10项的和
.
注.
表示不超过x的最大整数.
![](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/a54cbae4e0a13ab3c3fee29d9444f56c.png)
(1)求数列
![](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/3fcdef06601729a0b683e07daf131b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4c7bd4c927f41b6a86f9b06add02a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
注.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
您最近一年使用:0次
2022-04-21更新
|
1441次组卷
|
4卷引用:江苏省南通市基地学校2022届高三下学期第四次大联考数学试题
江苏省南通市基地学校2022届高三下学期第四次大联考数学试题江苏省宿迁市沭阳如东中学2022-2023学年高三上学期阶段测试(四)数学试题新高考基地学校2022届高三第四次大联考数学试题(已下线)押新高考第18题 数列-备战2022年高考数学临考题号押题(新高考专用)
9 . 已知正项等差数列
满足:
,且
成等比数列.
(1)求
的通项公式;
(2)设
,
是数列
的前n项和,若对任意
均有
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b48c9961d96b26ccfba412b667b5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9d985ae10825bc6ef93d5dfaf1fafb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c504b864a2dadcc1db404ff4bcaac396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65cabd89f7cbe31c771a7380711a935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-04-21更新
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9卷引用:江苏省盐城市阜宁县东沟中学2022届高三下学期第一次综合训练数学试题
江苏省盐城市阜宁县东沟中学2022届高三下学期第一次综合训练数学试题湖北省2022届高三下学期4月调研(二模)数学试题辽宁省东北育才双语学校2022届高三决胜高考最后一卷数学试题江苏省盐城市阜宁县东沟中学2022-2023学年高三上学期第一次综合训练数学试题黑龙江哈尔滨市第一二二中学-202届高三一模数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(5月31日)(已下线)三轮冲刺卷08-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)(已下线)考点15 数列综合问题-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)辽宁省铁岭市六校协作体2022-2023学年高三上学期第一次联考数学试题
10 . 已知数列
满足
,
,
.
(1)设
,
,求证:数列
为等差数列;
(2)求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb65a03cbd622222d928f911f9ac3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb882a35c06bed888729cd3b0cf0bad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5a133982e755a5cd52ef21bf95d251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460051e994f6e23bd5810a40f7bd21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
您最近一年使用:0次
2022-04-19更新
|
1027次组卷
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4卷引用:江苏省泰州市兴化市2022届高三下学期4月模拟考试数学试题
江苏省泰州市兴化市2022届高三下学期4月模拟考试数学试题湖北省天门中学2022届高三下学期适应性考试(二)数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(5月31日)广东省清远市华侨中学2023届高三上学期10月月考数学试题