1 . 设
,考虑一个含有
项的数列,其中每个数为0、-1或2.现将数列中的数两两相乘,再将这些乘积相加,这样得到的值为“和积值”.例如,取
,数列为0,-1,-1,2,那么乘积为
,
,
,
,
,
,和积值就为
.若一个数列含有2020项,则这个数列的最小和积值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e5270c151c0c9de54dd93e9687372c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e29d450e983dc5324fb1125bd7165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e29d450e983dc5324fb1125bd7165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3b9e0c5796d964c0dcb7e5f6e8156a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff028a1c8b062682400a5c66bf9d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3e33f3a8303606a6e4db783fee9c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3e33f3a8303606a6e4db783fee9c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c7e6d83d4088b72a36468947a35ed2.png)
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2 . 设
,
,若
,则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85319a950bf16b9388aa81a5b36b67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf27b31754829c0e8317cc065b818375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c6c0a39713d7a6e5a7632a9baca161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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解题方法
3 . 数列
的首项为
,前
项和为
,若
成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.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/db5714abe72dbf3fc3c8da134f4b5552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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名校
4 . 已知数列
,
是递增数列,则
的取值范围_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937d04e6d1fb8a8c61a919dc44c954f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-01-04更新
|
724次组卷
|
5卷引用:数学奥林匹克高中训练题_47
解题方法
5 . 设数列
满足
,且
,则通项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c2dc3e8291037e6b180d67b137c37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f200a5483af0cfa8f56068585cba52d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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名校
6 . 已知数列
的前n项和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559a339fa0fd3c11f2e45fa9e9fe1693.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5730fc489344c43cc6250d4f1bb9c2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559a339fa0fd3c11f2e45fa9e9fe1693.png)
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2024-03-14更新
|
276次组卷
|
2卷引用:第八届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
7 . 设正数列
满足
,且
,则
的通项公式是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb93df462dde10cc60418cbccaaeb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405dc9bac8fb39d3f2a0d944e5bf4731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e6dcb540f7df224600858f30d72efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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名校
8 . 已知数列
和
中,
,
是公比为
的等比数列;记
若不等式
对一切
恒成立,求实数
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/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a731b7eff81021baee07b9ea6f138bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e2f964bb664deba92b0f9ea5f0d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-08-16更新
|
179次组卷
|
3卷引用:第十二届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
第十二届高一试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)江苏省常州市高级中学2019-2020学年高三下学期二模适应性训练(二)数学试题(已下线)考点10 等比数列-2022年高考数学一轮复习小题多维练(新高考版)
9 . 已知
,则数列
的最小值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095540ea7ceec5d8c686147f3701fe38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
10 . 若数列
满足
(
为常数),则称数列
为等比和数列,
称为公比和,已知数列
是以3为公比和的等比和数列,其中
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb4c2355ce193435dc15fdc006fd237.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c17008d239a4f8d3fc61eb9042a725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cefeddf71dca8ae824328df3f0e5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb4c2355ce193435dc15fdc006fd237.png)
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2024-03-23更新
|
135次组卷
|
2卷引用:第六届高一试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)