名校
解题方法
1 . 已知公差不为零的等差数列
满足:
,且
是
与
的等比中项,
(1)求数列
的通项公式;
(2)设数列
满足
,
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb9a10fb4c527e66cff264ea2aee84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be9c9b05fd84ac9256d49a5a553af5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
解题方法
2 . 已知数列
的奇数项是公差为
的等差数列,偶数项是公差为
的等差数列,
是数列
的前
项和,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7826eb4aa860ff212f1bdc9ff310c901.png)
(1)若
,求
;
(2)已知
,且对任意的
,有
恒成立,求证:数列
是等差数列;
(3)若
,且存在正整数
,使得
,求当
最大时,数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.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/7826eb4aa860ff212f1bdc9ff310c901.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fceb89dab24237747cfceb6bde8cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412e3609c9490d61a3720ed638eae8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71a59fa91c73b84d74c8c3c8f33a0d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23203e6fe763edf125c6e168a6918587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db7584f54ec68298b29efb662a9a777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2017-06-23更新
|
502次组卷
|
4卷引用:4.2.2 等差数列前n项和2课时
(已下线)4.2.2 等差数列前n项和2课时江苏省南菁高级中学2016-2017学年高一下学期期中考试数学试题2020届江苏省南通市高三下学期4月高考模拟数学试题(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮
11-12高二上·湖南湘西·阶段练习
3 . 设数列
的前
项和为
,且
;数列
为等差数列,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96008cebfce08da2703bb0ecef7097c3.png)
(I)求数列
的通项公式;
(II)若
,
为数列
的前
项和,求证:
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecd8203c2dde0baed652dbaeb0e0423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2c97f55d9ffac66e05017b38c05b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96008cebfce08da2703bb0ecef7097c3.png)
(I)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(II)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921ec5f6a927c14f93a9a2bc24b96acf.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/a0cb2eb96749f942405162047de63664.png)
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4 . 已知公差不为零的等差数列
的前3项和
,且
、
、
成等比数列.
(1)求数列
的通项公式及前
项的和
;
(2)设
为数列
的前
项和,证明:
;
(3)对(2)问中的
,若
对一切
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5170584604571b5e1afd5ece941e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](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/3a5c15ab921f4f00c0da6b451db2ba40.png)
(3)对(2)问中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0515e305425472fb60b6f3c8c834c1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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10-11高一下·湖北宜昌·期中
5 . 本小题满分12分)已知等差数列
的前
项和
,且
.
(1)求
的通项公式;
(2)设
,求证:
是等比数列,并求其前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/7e431d92c5041fa44373c9df45c7309f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e6e2e198904f054456646f4352aa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.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
2016-12-03更新
|
842次组卷
|
5卷引用:2011-2012学年度广东省中山一中高二期中理科数学试卷
(已下线)2011-2012学年度广东省中山一中高二期中理科数学试卷甘肃省庆阳二中2017-2018学年高二第一次月考数学试卷(已下线)2010-2011学年湖北省长阳一中高一第二学期期中考试理科数学卷2014-2015学年福建省德化一中高一下学期期末质量检查数学试卷新疆自治区北京大学附属中学新疆分校2018-2019学年高一下学期期中考试数学试题
名校
6 . 已知等差数列
的公差
它的前
项和为
,若
且
成等比数列.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2da4105d60208e79df41a22987ba35.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/63ded6901d7b1e7dde28be1e676885a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea68ba197cb8727562208a44d36e8144.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051e50e9a3fb2a8c63e171eaed229b2d.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/64fe8499fbfb72cc31413a9148e6cf31.png)
您最近一年使用:0次
2016-12-03更新
|
1461次组卷
|
5卷引用:2014-2015学年湖北长阳县第一高中高二上学期期中考试理科数学试卷
名校
7 . 已知公差不为零的等差数列
,满足
成等比数列.
(Ⅰ)求数列
的通项公式;
(Ⅱ)若
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc145578a0183ba4d80b10c072b7f188.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d787a9e10d72bba6e3003db3a2dd35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4745c3a29a66285e380c867bd2dc99.png)
您最近一年使用:0次
2016-12-03更新
|
553次组卷
|
2卷引用:湖南省长沙市第一中学2021-2022学年高二上学期12月第二次阶段检测数学试题
解题方法
8 . 已知等差数列
的各项互不相等,前两项的和为10,设向量
,且
.
(1)求数列
的通项公式;
(2)若
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f4018eedc35bfcfc8ad3a1902eef29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d0fdc271e4511ee0ba03495ede2284.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72c413ed9091a9cfb58afdaa596c227.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/38bd70d785ad51a9a435d6d0f3e4769e.png)
您最近一年使用:0次
10-11高二下·湖南·阶段练习
9 . 设数列
的前
项和为
,且
;数列
为等差数列,且
.
(1)求数列
的通项公式;
(2)若
为数列
的前项和,求证:
.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecd8203c2dde0baed652dbaeb0e0423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ec455a9302064c51dfa8b0a1513356.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03464fea1f4769b497c88bfff413ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0cb2eb96749f942405162047de63664.png)
您最近一年使用:0次
2010·河北邯郸·二模
解题方法
10 . 设数列
为等差数列,且
,
,数列
的前
项和为
,
且
;
(Ⅰ)求数列
,
的通项公式;
(Ⅱ)若
,
为数列
的前
项和. 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/2010/7/3/1569778210455552/1569778215682048/STEM/a86a0e5e28e54071aeda57ea59d5627c.png?resizew=52)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96008cebfce08da2703bb0ecef7097c3.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73e06605cc93d9844b02ca51e90433e.png)
![](https://img.xkw.com/dksih/QBM/2010/4/26/1569704590516224/1569704596168704/STEM/a99c37530fc045c1a150d1e737b81f6d.png?resizew=179)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46c4e3c379e5d8516494d6ff3caef58.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/9ed5b54a11649a1ff4b335a141b420d9.png)
您最近一年使用:0次