名校
1 . 已知等差数列
的公差为
,集合
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a033d03631fe159d5c89025365fca62c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d620c72ee3c16c8fa2c1b0e45882c3a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4753f4a4456d0df13843b71015bfa14.png)
A.-1 | B.![]() | C.0 | D.1 |
您最近一年使用:0次
名校
解题方法
2 . 已知正项数列
前
项和为
,且满足
,
.
(1)求数列
的通项公式;
(2)若数列
满足
,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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5400637a79e6e7af3ae5214be34a615.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
3 . 已知数列
中,
且
,则
( )
![](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/ca179b51a0cff1f81d951b508a77b3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5edade76c845f5e0e5a3aed8af3436.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024高二·全国·专题练习
4 . 已知
是数列
的前n项和,
,
,不等式
对任意的
恒成立,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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce14743fa38b7bbf82358655138e8159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ce75a36971dbfd7ecb0bb97cff61ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
5 . 已知数列
为等差数列,
,前
项和为
,满足:当
且
时,
.
(1)求
的通项公式;
(2)定义集合
且
,记
的元素个数为
,数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630df1e98d73e9c43bd8378991534dd6.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/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3b59acccb7bb76ced518b36426b7c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eea3608cb72fcea4f8c7e93d6a0d44f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)定义集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea5a0c272f0c5a78330b21d5b225db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa850d30dc0658e9768cdd0eb176fe30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3cf40c3b4e46c1c52d7eadff64a9ec4.png)
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6 . 已知数列
的前n项和为
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82b7afbfc50eb2bbb34b8760071e8a0.png)
(1)求
;
(2)若
,求数列
的前1012项和
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82b7afbfc50eb2bbb34b8760071e8a0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08956de999dbddf9e42111a3d7cd9012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee6b547a3be248c012cc94abf603c09.png)
您最近一年使用:0次
2024-05-12更新
|
780次组卷
|
6卷引用:4.3.2等比数列的前n项和公式(2)
(已下线)4.3.2等比数列的前n项和公式(2)(已下线)4.2.2等差数列的前n项和公式(1)(已下线)专题1 数列奇偶项、子数列求和压轴题【讲】(高二期末压轴专项)河南省九师联盟2024届高三下学期5月联考数学试题甘肃省武威第六中学2023-2024学年高三下学期第五次诊断数学试卷辽宁省沈阳铁路实验中学2024届高三第八次模拟考试数学试题
7 . 已知数列
满足
,
是公差为
的等差数列.
(1)求
的通项公式.
(2)令
,求数列
的前n项和
.
(3)令
,是否存在互不相等的正整数m,s,n,使得m,s,n成等差数列,且
,
,
成等比数列?如果存在,请给出证明;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4123422b5a6621da6a3214aa8c3e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099a64d86bd0b4602578d910322adc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbc3b9ad99da1f31b0a598f6754c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a64999ed95ead1707c7aca94cbbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8f3b95cf758b56f0b94a261272fe82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8384f67b3cd493b9b1062908c0128214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82a4d8875890196df49fc7d6944161e.png)
您最近一年使用:0次
2024-05-11更新
|
260次组卷
|
3卷引用: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)
(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)广东省顺德区北滘中学2023-2024学年高二下学期期中考试数学试卷广东省佛山市桂城中学2023-2024学年高二下学期第二次段考数学试卷
名校
解题方法
8 . 已知数列
的前n项和为
.若对每一个
,有且仅有一个
,使得
,则称
为“X数列”.记
,
,称数列
为
的“余项数列”.
(1)若
的前四项依次为0,1,
,1,试判断
是否为“X数列”,并说明理由;
(2)若
,证明
为“X数列”,并求它的“余项数列”的通项公式;
(3)已知正项数列
为“X数列”,且
的“余项数列”为等差数列,证明:
.
![](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/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42dd37c118e64c46c7fc37e21081745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450706c32e58d9e6ad2f14aabf9e81ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d255ea8e125b603d6b640bdf4a804922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)已知正项数列
![](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/771ca8c38c8a1646c83481a1d2bcfdfa.png)
您最近一年使用:0次
2024-05-07更新
|
1480次组卷
|
4卷引用:专题14 学科素养与综合问题(解答题19)
(已下线)专题14 学科素养与综合问题(解答题19)江苏省南京市2024届高三第二次模拟考试数学试题黑龙江省牡丹江市第三高级中学2024届高三下学期第四次模拟数学试卷湖北省襄阳市第五中学2024届高三下学期第四次适应性测试数学试题
9 . “孙子定理”又称“中国剩余定理”,最早可见于我国南北朝时期的数学著作《孙子算经》,该定理是中国古代求解一次同余式组的方法,它凝聚着中国古代数学家的智慧,在加密、秘密共享等方面有着重要的应用.已知数列
单调递增,且由被2除余数为1的所有正整数构成,现将
的末位数按从小到大排序作为加密编号,则该加密编号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00710f703caaf1b8721b60c07b88d097.png)
A.1157 | B.1177 | C.1155 | D.1122 |
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2024·全国·模拟预测
解题方法
10 . 已知数列
满足
,若数列
的前
项和为
,不等式
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/1ea29a78db01eee98947b8f8d7a0d11d.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de295470b3079d6c2724731f7405da8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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