名校
1 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.在无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等差数列.
(1)若
为1阶等比数列,
,求
的通项公式及前
项和;
(2)若
为
阶等比数列,求证:
为
阶等差数列;
(3)若
既是4阶等比数列,又是5阶等比数列,证明:
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7f4b6e82924087d9fa4523cd509d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a08caf919ff9fa62e20d91af57c401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0831836c71efc1b1ffdb73073da2a2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-03-10更新
|
940次组卷
|
4卷引用:河南省TOP二十名校2024届高三下学期质检一数学试题
2 . 甲、乙两人进行一场友谊比赛,赛前每人记入3分.一局比赛后,若决出胜负,则胜的一方得1分,负的一方得
分;若平局,则双方各得0分.若干局比赛后,当一方累计得分为6时比赛结束且该方最终获胜.令
表示在甲的累计得分为i时,最终甲获胜的概率,若在一局中甲获胜的概率为
,乙获胜的概率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec818fc0754296163206e1e8870f9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7412fd1be21e4eaf388963a82ac2b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20ed5d99d1f0e082460a300da99b32d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-10更新
|
1462次组卷
|
6卷引用:河南省TOP二十名校2024届高三下学期质检一数学试题
河南省TOP二十名校2024届高三下学期质检一数学试题河南省TOP二十名校2024届高三下学期质检一数学试题河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷(已下线)7.1.1条件概率7.1.2全概率公式 第三练 能力提升拔高(已下线)【讲】专题10 数列与其它知识的交汇问题黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期得分训练数学试题(四)
名校
解题方法
3 . 已知数列
满足
,正项数列
满足
.当
时,记
.
(1)证明:
是等比数列;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a062612f4052dede47b4f6cd00a447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9783fe465f1267a4388bf7e30a97ad69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a59d8a8d1f71d3c825de3cee07cb04.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d96758e7997e9263c4b3e0fe4b862d7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99938dc5ca6676b7711080bf3b100dbf.png)
您最近一年使用:0次
4 . 已知正项数列
的前n项和为
,且满足 .
(1)求
的通项公式;
(2)已知
设数列
的前n项和为
当n∈
时,
,求实数 λ 的范围.
条件:①
,且
等差数列;②
; ③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d95c2bca9a6f2ae20e2514dbb8a7ab.png)
请从这三个条件中任选一个,并将其序号填写在答题卡对应位置,并完成解答.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae734ad099abbb2f7efe7d7a6a4169fd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add02169a8f58417880df4e302a7c498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ff73adcee207aab99fa195e19ae15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09396ce60d49d7131687cdca993e9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fa38d95b4c4b52228a77e87b2de484.png)
条件:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6cbbec0f900da8864d00e396893c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545d9746ca31e6928b745714601628ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed65adb9faff38cfa1a8b5dfcb1cee1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83bd46c8ed4549e63dacd6ab96f1f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d95c2bca9a6f2ae20e2514dbb8a7ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
您最近一年使用:0次
2024-01-03更新
|
397次组卷
|
2卷引用:河南省许济洛平2024届高三上学期第二次质量检测数学试题
5 . 某公司计划在12年内每年对某产品的广告投入(单位:万元)等于上一年的1.5倍再减去2.已知第一年(2018年)该公司对该产品的广告投入为5万元,则按照计划该公司从2018年到2028年(含2028年)对该产品的广告总投入约为( )(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f246cfaa51b080059814ad412395812.png)
A.215万元 | B.219万元 | C.153万元 | D.154万元 |
您最近一年使用:0次
名校
解题方法
6 . 在当前市场经济条件下,私营个体商店中的商品,所标价格
与其实际价值之间,存在着相当大的差距.对顾客而言,总是希望通过“讨价还价”来减少商品所标价格
与其实际价值的差距.设顾客第
次的还价为
,商家第
次的讨价为
.有一种“对半讨价还价”法如下:顾客第一次的还价为标价
的一半,即第一次还价
,商家第一次的讨价为
与标价
的平均值,即
;…;顾客第
次的还价为上一次商家的讨价
与顾客的还价
的平均值,即
,商家第
次的讨价为上一次商家的讨价
与顾客这一次的还价
的平均值,即
.现有一件衣服标价1200元,若经过
次的“对半讨价还价”,
与
相差不到
元,则
最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87fa84133cfd73665124231788a13e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9706612eb69f144af8a99a8425f6f752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402f55b4b8c18659a1f20a3056f16fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9d41db805f5235ec4b69e436690222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb2afbf35d798514b2ff7f5c17e020b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402f55b4b8c18659a1f20a3056f16fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bcba1d48ef9ae029558dd9ae50ae69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.4 | B.5 | C.6 | D.7 |
您最近一年使用:0次
2022-02-23更新
|
681次组卷
|
7卷引用:河南省五市2023届高三二模数学试题(理)
河南省五市2023届高三二模数学试题(理)河南省三门峡市湖滨区等5地2023届高三第三次大练习数学(理)试题浙江省名校协作体2021-2022学年高二下学期开学考试数学试题浙江省台州市书生中学2021-2022学年高二下学期起始考数学试题(已下线)4.3等比数列B卷(已下线)重难点专题03 等比数列及其前n项和-2022-2023学年高二数学重难点题型分类必刷题(人教B版2019选择性必修第三册)(已下线)情境3 促进经济发展