1 . 已知数列
的奇数项是首项为1的等差数列,偶数项是首项为2的等比数列.数列
前
项和为
,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1afb2ab393153baf1dbb0b7457254.png)
(1)求
;
(2)求数列
的通项公式及数列
的前2k项和
;
(3)在数列
中,是否存在连续的三项
,按原来的顺序成等差数列?若存在,求出所有满足条件的正整数
的值;若不存在,说明理由
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1afb2ab393153baf1dbb0b7457254.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec70234b2136c08abd7a59726cc0ea0.png)
(2)求数列
![](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/1254067b56565394384de5be7b8f3ec1.png)
(3)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91239c38be30570f5905f56d03b0ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 已知数列
是公差为
的等差数列,若它的前
项的和
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5596e3d616cd804ad9a29a98b720831d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079f16bbd0704ecb6e5e44c5725af1d9.png)
A.若![]() ![]() ![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
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|
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2卷引用:江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题
名校
解题方法
3 . 已知数列
的前
项和为
,若数列
满足:①数列
项数有限为
;②
;③
,则称数列
为“
阶可控摇摆数列”.
(1)若
,请判断数列
是否为“
阶可控摇摆数列”?若是,请求出
的值;若不是,请说明理由;
(2)若等比数列
为“10阶可控摇摆数列”,求
的通项公式;
(3)若等差数列
为“
阶可控摇摆数列”,且
,求数列
的通项公式.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4ed75729a7f7a2d5a3d9f7293c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781342df475217b47b622044a112f1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353cc14af0e73b3ef2fb65ad1ec07d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917e9c3724f02de6ffd0ed8252ab2166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84f10b80ce3402ac5369e6a1465d9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa22ba45c62adc96ffe508594edd6900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
4 . 已知数列
是公差不为零的等差数列,且
,
,
成等差数列,
,
,
(
)成等比数列,
.
(1)求
的值及
的通项公式;
(2)令
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a2fc7063bcdce2bee4cb0f4d748d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a52616446c7d86d7d216a522d7ac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58da100fbf2f8a10c1366ec7bb06252a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54241b0eb7802c5425a1ba7c4d6e249a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531e77e1a45032cefac08b27c06516e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7039c048ae6d04ff63211851ae216d.png)
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解题方法
5 . 数列
有
项,
,对任意
,存在
,若
与前
项中某一项相等,则称
具有性质
.
(1)若
,求
可能的值;
(2)若
不为等差数列,求证:
中存在满足性质
;
(3)若
中恰有三项具有性质
,这三项和为
,使用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccf7e4dc2f2528b70a7b6920a0360de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c439f52fd3e4c4f6c9872041044d7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a45cd3046323db116ec970be533d2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)若
![](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/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470a3b303d8e0a78a68dde895a46bb88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b07d62c4025696b4c648db0c3dd67bf.png)
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解题方法
6 . 已知数列
,
满足
,
,且
是等差数列.
(1)若
是公比为2的等比数列,求
的通项公式;
(2)记
,
分别为
,
的前
项和,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def3c149882e1561bc00295188b5c3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec12a9a60f82467bf7bf834a9a9b1f7.png)
(1)若
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20a8929eae98e58065aea047a371899.png)
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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
|
255次组卷
|
3卷引用: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
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(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)
名校
8 . (1)已知k,
,且
,求证:
;
(2)若
,且
,证明:
;
(3)设数列
,
,
,…,
是公差不为0的等差数列,证明:对任意的
,函数
是关于x的一次函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e10e0bb04d7d261d880aea655e19db1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030d7dbc61a27892cd24b1c4d21745ee.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dbbfed8a6279c3c233cdd1795946ed.png)
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9 . 已知数列
的前
项和为
,若数列
满足:①数列
项数有限为
;②
;③
,则称数列
为“
阶可控摇摆数列”.
(1)若等比数列
为“10阶可控摇摆数列”,求
的通项公式;
(2)若等差数列
为“
阶可控摇摆数列”,且
,求数列
的通项公式;
(3)已知数列
为“
阶可控摇摆数列”,且存在
,使得
,探究:数列
能否为“
阶可控摇摆数列”,若能,请给出证明过程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4ed75729a7f7a2d5a3d9f7293c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1798fb0c31c65218cd20e07320a17d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdaa641d2e7e17904c61ff7245a5cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7364bbda64feeb4d448f9316d4c67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa22ba45c62adc96ffe508594edd6900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca8076f0553088afded57b48009d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae2ea9de54e074c145b8259f6c55e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2024-03-21更新
|
1434次组卷
|
6卷引用:江西省2024届高三下学期二轮复习阶段性检测数学试题
江西省2024届高三下学期二轮复习阶段性检测数学试题山东省淄博市实验中学2023-2024学年高二下学期第一次月考(3月)数学试卷吉林省白山市2024届高三第二次模拟考试数学试题(已下线)数学(广东专用01,新题型结构)吉林省通化市梅河口市第五中学2024届高三下学期二模数学试题(已下线)压轴题05数列压轴题15题型汇总-1
10 . 已知数列
满足:
,正项数列
满足:
,且
,
,
.
(1)求
,
的通项公式;
(2)已知
,求:
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f51d2d57bb9a400d2051f325b614419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68783e644e41b5a3aac4e81d44ba5f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffaa768f1232ff14bcd2cdd438ce53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1273751a0b5a984cf01c2d0e00e474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb27d03d22ec55dbf33d6d9d3c44854f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e0c7c3411a1f192200d24f7161d4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ca23ce02583bd8fe3b9d06d99e0e3c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dacb1f9b17bb176ab57962aa783179ad.png)
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2024-03-03更新
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