1 . 已知数列
的前
项和为
,
,
.
(Ⅰ)求数列
的前
项和为
;
(Ⅱ)求数列
的通项公式;
(Ⅲ)令
,求数列
的前
项和
.
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59368e5ae709bdb9b6ddec2bfa3afde.png)
(Ⅰ)求数列
![](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)
(Ⅱ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅲ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.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)
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名校
解题方法
2 . 已知正项数列
的前n项和为
,且
是4和
的等比中项,数列
,其前n项的和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a8462c07c0143853c1bec52084360e.png)
__________ .
![](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/23016d1186ebefd8d67387f43f100229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e722d1cb06e597485399a64c75b14a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a8462c07c0143853c1bec52084360e.png)
您最近一年使用:0次
2020-07-20更新
|
638次组卷
|
2卷引用:四川省遂宁市船山区第二中学校2020届高三高考适应(二)考试数学(文)试卷
名校
解题方法
3 . 已知数列
为等差数列,数列
为等比数列,若
,
,
.设
,
是数列
的前
项的和.
求数列
和
的通项公式;
求数列
的前
项的和
.
![](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/7c5a7a17a394e868e0acd1803a9ab795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494a1444abd3f9441b30d999f65b3203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368d8990b75b73480fefdbdb6352d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](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/1f53190d6ead827a6338b9de847aeaf1.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
4 . 已知数列
与
满足
,
.
(1)若
,求数列
的通项公式;
(2)若
,且数列
是公比等于2的等比数列,求
的值,使数列
也是等比数列;
(3)若
,且
,数列
有最大值
与最小值
,求
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/998926638c7b8a50714455fb2c81693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10226aabc54614cdc01a68b1a60a5770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078a5f2f480f345ecc5a13bd09ce539f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d96beb63c117094ca155b15c72ac28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de524a163912682710d2a1918d66ff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467f61f8d38c71fcb30f3f16d88650d7.png)
您最近一年使用:0次
2020-02-08更新
|
429次组卷
|
2卷引用:2016届上海市崇明县高三第二次高考模拟(文)数学试题
名校
5 . 设满足以下两个条件的有穷数列
为
阶“期待数列”:①
;②
.
(1)若等比数列
为
阶“期待数列”
,求公比
;
(2)若一个等差数列
既是
阶“期待数列”又是递增数列
,求该数列的通项公式;
(3)记
阶“期待数列”
的前
项和为
,求证;数列
不能为
阶“期待数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39aa494487b73dbac3d6b868d822fddd.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1306375a0fec4eb4bf3f07992f6716e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若一个等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1306375a0fec4eb4bf3f07992f6716e.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45581140d4687ff796b7cc53609702e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea210b22ee669a90173c4bd61c39596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500c42aa6116832f6ef1fe41d3d214bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
6 . 已知数列
和
满足
,
,
.
(1)证明:
是等比数列,
是等差数列;
(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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee423d15df9804185bf5242e75f501cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d807a81b4f3c1503bc8447f437bf91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326a11bac583ee0eda8ebea723c103e2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec12a9a60f82467bf7bf834a9a9b1f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a9cb389ad8e9aa57d822096810ea1c.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
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7 . 已知数列
共有
项,满足
,且对任意
、
,有
仍是该数列的某一项,现给出下列
个命题:(1)
;(2)
;(3)数列
是等差数列;(4)集合
中共有
个元素.则其中真命题的个数是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0691113b206b6ccc9605838480d15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9534f31da88b0ee71c38aac82f2922a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8692a851a72427d95eac78f2efd9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd67cf18bd35149475d35f1c603ad59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412085a55df5ec90bda732f650ee11ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d244b23bc56588813db957c1ded41ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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8 . 已知
是数列
的前
项和,对任意
,都有
;
(1)若
,求证:数列
是等差数列,并求此时数列
的通项公式;
(2)若
,求证:数列
是等比数列,并求此时数列
的通项公式;
(3)设
,若
,求实数
的取值范围.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4faa5d8f3b8d5f59910ef3e885abe4fc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46db680bc60929939e0f09990c03583e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac5c639aa5cd63ab86b2b0d9a23c998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6788d3dbbd2d5f865db8d414375339e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ba3d72887756e8d222e0e3ae6aff5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75330ac9e51cdef4bc61012551e1d00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-12-08更新
|
766次组卷
|
3卷引用:2018年上海市复旦附中高三5月三模数学试题
名校
9 . 在数列
中,已知
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb298f2db5dc57d6fb335388baad975.png)
(1)求数列
的通项公式;
(2)设数列
满足
,且数列
前
项和为
,若
,对
恒成立,求实数
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46b1623a64c6cdfbda506fba57951d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb298f2db5dc57d6fb335388baad975.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ab820f145b26e851aeeb6f68514748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.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/8531e4f0e1692f18f96118f20de154de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
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10 . 等差数列
的前n项和为
,
,
,
对一切
恒成立,则
的取值范围为____ .
![](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/99ebeece107bf3b1ae267e068d3f42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e4fef2ea80b0a9b4fe41dba80a4fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed60d996b544157e7e470167d20107eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2019-01-30更新
|
1937次组卷
|
7卷引用:【校级联考】广东省华南师范大学附属中学、广东实验中学、广雅中学、深圳中学2019届高三上学期期末联考数学(文)试题
【校级联考】广东省华南师范大学附属中学、广东实验中学、广雅中学、深圳中学2019届高三上学期期末联考数学(文)试题【校级联考】广东省华附、省实、广雅、深中2019届高三上学期期末联考数学(文)试题安徽省部分省示范中学2018-2019学年高一下学期期中数学试题黑龙江省哈尔滨师范大学青冈实验中学校2019-2020学期高三上学期开学考试(8月)数学(文)试题(已下线)专题7.7 数列与数学归纳法单元测试卷(测)-2021年新高考数学一轮复习讲练测黑龙江省大庆中学2020-2021学年高三上学期期中考试数学(文)试题河南省焦作市温县第一高级中学2021-2022学年高三上学期11月月考文科数学试题