1 . 若数列
满足
(
为正整数,
为常数),则称数列
为等方差数列,
为公方差.
(1)已知数列
,
的通项公式分别为:
,
,判断上述两个数列是否为等方差数列,并说明理由;
(2)若数列
是首项为1,公方差为2的等方差数列,在(1)的条件下,在
与
之间依次插入数列
中的
项构成新数列
:
,
,
,
,
,
,
,
,
,
,……,求数列
中前30项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595955aa3a2670abcd60c78a5086f2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19814dff8cdcec0e1a9eab38f4f16e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803d745499bb0ea7cd963cb2f4c871e.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4741eb4c177d75ca74fe2d36e52ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf52946ef832dd2fa7a82dcd6d1bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23cabc65fcefdd191930fbfa89cf125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8553a873958eb9d14c89c59ab5c317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a2fc7063bcdce2bee4cb0f4d748d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314bd1d7a6e070f4f2428f9a321804e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c992eaf396ef52255403bfca119e032c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9839f07d78de3e6d161e4e1eff25b9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9a8ceb6e6214002bbdbb71e7828110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ee8fc80a880ccceac24aa739fac39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f550f4135c46fbfb0c001e662cd8ff6.png)
您最近一年使用:0次
22-23高二下·上海·期末
2 . 设满足以下两个条件的有穷数列
为n(
)阶“期待数列”:
①
;
②
.
(1)分别写出一个单调递增的3阶和4阶“期待数列”;
(2)若某
(
)阶“期待数列”是等差数列,求该数列的通项公式;
(3)记n阶“期待数列”的前k项和为
(
),试证:
(i)
;
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec0b97655e6bd7004df04457c493ac.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4830a6ec5e0ffd7074b854b4ecdc19.png)
(1)分别写出一个单调递增的3阶和4阶“期待数列”;
(2)若某
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394aee19f94c2b70fcce1d69b31dc7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699dfd96d64e59252e384847629c7a75.png)
(3)记n阶“期待数列”的前k项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541e541ef98215381bb9120cd39020ca.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7575a54621b480d9d1e0efa5935d8f47.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fbfe923e23263b5ae34ee75bb430ab.png)
您最近一年使用:0次
3 . 由函数确定数列
,
,若函数
的反函数
能确定数列
,
,则称数列
是数列
的“反数列”.
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881767379325c886f9d806ff4fa4ccf3.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/034ba25825c13725931c483aa47c9363.png)
(2)对(1)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecaa3a6251533babfaa59450b4ff0fa.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd45ab1f53a00a0a2dd8245ab7d2eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2174394deab39443edad16adb40a652b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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22-23高二下·上海·期末
4 . 对于任意的
,若数列
同时满足下列两个条件,则称数列
具有“性质m”:
①
;②存在实数M,使得
成立.
(1)数列
、
中,
,判断
、
是否具有“性质m”;
(2)设各项为正数的等比数列
的前n项和为
,且
,
,数列
是否具有“性质m”,若具有,请证明你的猜想,并指出M的范围;若不具有,理由?
(3)若数列
的通项公式
.对于任意的
(
),数列
具有“性质m”,且对满足条件的M的最小值
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75a9da38151496ca2adce84a977b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
(1)数列
![](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/ef91b91fc7ac183837bd7c6799f19c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设各项为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12baad2468950ea89781e38432d88f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ab4706be6b3854b9c30ab609e5da68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9050ccff2f6fea858342b0fb290ad7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191d51029a192d504bf1b736029f82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
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名校
解题方法
5 . 若数列
满足:
,且
,则称
为一个X数列. 对于一个X数列
,若数列
满足:
,且
,则称
为
的伴随数列.
(1)若X数列
中,
,
,
,写出其伴随数列
中
的值;
(2)若
为一个X数列,
为
的伴随数列.
①证明:“
为常数列”是“
为等比数列”的充要条件;
②求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8ba9ab2f7cce1c14159d936508531e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf3c946a47b7c3b46a7e25a7dbee5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若X数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58365ff21052f2f978c11844b002b933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2da0ff9dc73d62f8162fc3de186150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8ae4555eacf411d0a8867d9970668.png)
(2)若
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
①证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067eff9b6d48fd98c3400188247e04b1.png)
您最近一年使用:0次
2023-08-16更新
|
592次组卷
|
6卷引用:北京大学附属中学2022-2023学年高二下学期期末练习数学试题
北京大学附属中学2022-2023学年高二下学期期末练习数学试题(已下线)第4章 数列单元检测(提优卷)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)【北京专用】专题01数列(第一部分)-高二上学期名校期末好题汇编北京市第五中学2024届高三上学期10月月考数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编
名校
解题方法
6 . 数列
:
,
,…,
满足:
,
,
或1(
,2,…,
),对任意i,j,都存在s,t,使得
,其中
且两两不相等.
(1)若
,直接写出下列三个数列中所有符合题目条件的数列的序号:
①1,1,1,2,2,2;②1,1,1,1,2,2,2,2;③1,1,1,1,1,2,2,2,2
(2)记
,若
,证明:
;
(3)若
,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/d8dc3192c861a4cc44da88f656ae7aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564e60383b05d2e0ee94a733742ae424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631c6879b8799ed0f1aefbf28bf988f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631c70b687b22d032d1cc5050cfc07dc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
①1,1,1,2,2,2;②1,1,1,1,2,2,2,2;③1,1,1,1,1,2,2,2,2
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb1eff85b93cd753c2a3a4fb9603221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afa6e51b3b27c3edb330cd7f190b6cf.png)
您最近一年使用:0次
2023-08-05更新
|
738次组卷
|
5卷引用:北京市海淀区清华大学附属中学2022-2023学年高二上学期期中考试数学试题
名校
7 . 给定正整数k,m,其中
,如果有限数列
同时满足下列两个条件.则称
为
数列.记
数列的项数的最小值为
.
条件①:
的每一项都属于集合
;
条件②:从集合
中任取m个不同的数排成一列,得到的数列都是
的子列.
注:从
中选取第
项、第
项、…、第
项(
)形成的新数列
称为
的一个子列.
(1)分别判断下面两个数列,是否为
数列.并说明理由!
数列
;
数列
.
(2)求
的值;
(3)求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff8f43f54aaab94d126c2ed7c929196.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/b33bf403c186b3c6747b2d9d1dd75990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33bf403c186b3c6747b2d9d1dd75990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733309155391786ce67cf7becf69cfdc.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8297742318e91be10074c89f212bc.png)
条件②:从集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8297742318e91be10074c89f212bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
注:从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6d8698bc7a9af6c0e9e2b7fb8b240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02034a7c04920a212f7974cd64dde9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823953737f36a700af348506ee8c678b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)分别判断下面两个数列,是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc0c923d538857536c1d74635147369.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8f0c365d19e8120876cd2dcc22f215.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa0ced8f2185d0f51a3b44cc247d302.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c118e992e32545ff658a95c284165cd.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db133f4329ff1231e7cd04148651d48b.png)
您最近一年使用:0次
2023-08-02更新
|
442次组卷
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2卷引用:北京市清华附中2022-2023学年高二下学期期末数学试题
8 . 若数列
满足
,则称数列
为“平方递推数列".已知数列
中,
,点
在函数
的图象上,其中n为正整数,
(1)证明:数列
是“平方递推数列”,且数列
为等比数列;
(2)设
,
,
求数列
的前10项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77eb4367983d955a4f070045d1290c9.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/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44042d110ad8bf676c2785c2b1f9a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12aeb2e34f029aefea75cccaa86eaa0.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2297648930c7d3a3a479893df751004.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c5b10914f5369cfecdd6614ec1d6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8458041b280f09b0bbf278fcc04ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e96143e2c91a5f6ef5446005640cbb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3cf6f2bbe20a404fea41a4d2b1c4c7.png)
您最近一年使用:0次
2023-07-24更新
|
900次组卷
|
7卷引用:山西省应县第一中学校2022-2023学年高二下学期期末数学试题
名校
解题方法
9 . 定义:若对任意正整数
,数列
的前
项和
都是整数的完全平方数,则称数列
为“完全平方数列”.
(1)若数列
满足
,判断
为是否为“完全平方数列”;
(2)若数列
的前
项和
(
是正整数),那么是否存在
,使数列
为“完全平方数列”?若存在,求出
的值;若不存在,请说明理由;
(3)试求出所有为“完全平方数列”的等差数列的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e95905e3f5d8dc67f74b44febb07353.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af66591a4140c35b3a9f01c9530d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ee9273cc82d57d99a21fb9c4953d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)试求出所有为“完全平方数列”的等差数列的通项公式.
您最近一年使用:0次
2023-07-21更新
|
331次组卷
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4卷引用:北京市怀柔区2022-2023学年高二下学期期末考试数学试题
北京市怀柔区2022-2023学年高二下学期期末考试数学试题江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题【北京专用】专题01数列(第一部分)-高二上学期名校期末好题汇编(已下线)专题02 等比数列4种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北京专用)
名校
解题方法
10 . 若数列
:
,
,
,
满足:对任意
,均有
成立,则称数列
为“
数列”.
(1)直接判断下面三个数列是否是“
数列”;①
:
,
,
,
;②
:
,
,
,
;③
:
,
,
,
;
(2)若“
数列”
:
,
,
,
满足
,证明:数列
是等差数列的充分不必要条件是
;
(3)求
的取值范围,使得存在非零实数
,对任意正整数
,数列
:
,
,
,
,
恒为“
数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b097651ff5fe206a43078269d005f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb81d8ef8d1d8a4d76ec37fa0afe3389.png)
(1)直接判断下面三个数列是否是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb81d8ef8d1d8a4d76ec37fa0afe3389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08be9681cf2689ffe4049c6dbb7b171f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c84e4232efa5f53727fa684117683c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c767ac27824662a6827bd3462575bbcf.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91022b25fa06ed1fa23a858582c5d689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e0e4d6f2921ff7bc5b55f0b20de376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d992261a422fcddad6ccb3798c77ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb81d8ef8d1d8a4d76ec37fa0afe3389.png)
您最近一年使用:0次