2>a 1a 3，选项C 正确．故选C.
[答案] C
5．(2020·江苏徐州期中)在公比q 为整数的等比数列{a n }中，S n
是数列{a n }的前n 项和．若a 1·a 4＝32，a 2＋a 3＝12，则下列说法错误的是( )
A ．q ＝2
B ．数列{S n ＋2}是等比数列
C ．S 8＝510
D ．数列{log 2a n }是公差为2的等差数列
[解析] 因为数列{a n }为等比数列，又a 1·a 4＝32， 所以a 2·a 3＝32，又a 2＋a 3＝12，
所以????? a 2＝4，
a 3
＝8，
q ＝2，
或???
?? a 2＝8，a 3
＝4，q ＝12.
又公比q 为整数，则????
?
a 2＝4，
a 3
＝8，
q ＝2，
即a n ＝2n ，S n ＝2×(1－2n )
1－2
＝2n ＋1－2.
对于选项A ，由上可得q ＝2，即选项A 正确；
对于选项B ，S n ＋2＝2n ＋1，S n ＋1＋2S n ＋2＝2n ＋2
2n ＋
1＝2，则数列{S n ＋2}是
等比数列，即选项B 正确；
对于选项C ，S 8＝29－2＝510，即选项C 正确；
对于选项D ，log 2a n ＋1－log 2a n ＝(n ＋1)－n ＝1，即数列{log 2a n }是公差为1的等差数列，即选项D 错误．
[答案] D
6．(2020·郑州二中期末)已知等差数列{a n }的公差d ≠0，且a 1，a 3，a 13成等比数列，若a 1＝1，S n 是数列{a n }的前n 项的和，则
2S n ＋16a n ＋3(n ∈N *)的最小值为( )
A ．4
B ．3
C ．23－2
D.92
[解析] ∵a 1＝1，a 1、a 3、a 13成等比数列， ∴(1＋2d )2＝1＋12d .得d ＝2或d ＝0(舍去) ∴a n ＝2n －1，
∴S n ＝n (1＋2n －1)
2＝n 2
， ∴2S n ＋16a n ＋3＝2n 2＋162n ＋2
.令t ＝n ＋1， 则2S n ＋16a n ＋3＝t ＋9t －2≥6－2＝4当且仅当t ＝3， 即n ＝2时等号成立，∴2S n ＋16
a n ＋3的最小值为4.故选A.
[答案] A 二、填空题
7．(2020·福建四地六校联考)已知等差数列{a n }中，a 3＝π
4，则cos(a 1＋a 2＋a 6)＝________.
[解析] ∵在等差数列{a n }中，a 1＋a 2＋a 6＝a 2＋a 3＋a 4＝3a 3＝34π，∴cos(a 1＋a 2＋a 6)＝cos 34π＝－22.
[答案] －2
2
8．(2020·浙江嘉兴教学测试)已知{a n }是公差为－2的等差数列，S n 为其前n 项和．若a 2＋1，a 5＋1，a 7＋1成等比数列，则a 1＝________，当n ＝________时，S n 取得最大值．
[解析] 因为a 2＋1，a 5＋1，a 7＋1成等比数列，
所以(a 5＋1)2＝(a 2＋1)(a 7＋1)． 又{a n }是公差为－2的等差数列， 所以(a 1－8＋1)2＝(a 1－2＋1)(a 1－12＋1)， 即(a 1－7)2＝(a 1－1)(a 1－11)，解得a 1＝19，
所以S n ＝19n －n (n －1)＝－n 2＋20n ＝－(n －10)2＋100. 因此，当n ＝10时，S n 取得最大值． [答案] 19 10
9．(2020·哈尔滨模拟)已知数列{a n }的前n 项和为S n ，S 1＝6，S 2
＝4，S n >0，且S 2n ，S 2n －1，S 2n ＋2成等比数列，S 2n －1，S 2n ＋2，S 2n ＋1成等差数列，则a 2020＝________.
[解析]
由题意得??
?
S 2
2n －1＝S 2n S 2n ＋2，
2S 2n ＋2＝S 2n －1＋S 2n ＋1.
∵S n >0，∴2S 2n ＋2＝S 2n S 2n ＋2＋S 2n ＋2S 2n ＋4，
即2
S 2n ＋2＝S 2n ＋
S 2n ＋4(n ∈N *)，
故{S 2n }是等差数列． 又由S 1＝6，S 2＝4，得S 4＝9，
∴{S 2n }是首项为2，公差为1的等差数列． ∴S 2n ＝n ＋1，即S 2n ＝(n ＋1)2， 故S 2n －1＝
S 2n S 2n ＋2＝(n ＋1)·(n ＋2)，
故S 2020＝10112，S 2019＝1011×1012， 故a 2020＝S 2020－S 2019＝－1011. [答案] －1011 三、解答题
10．(2020·成都测试)已知等差数列{a n }前三项的和为－9，前三项的积为－15.
(1)求等差数列{a n }的通项公式；
(2)若{a n }为递增数列，求数列{|a n |}的前n 项和S n .
[解] (1)设数列{a n }的公差为d ，则依题意得a 2＝－3，则a 1＝－3－d ，a 3＝－3＋d ，
∴(－3－d )(－3)(－3＋d )＝－15，解得d 2＝4，d ＝±2， ∴等差数列{a n }的通项公式为a n ＝－2n ＋1或a n ＝2n －7.
(2)由题意及(1)得a n ＝2n －7，∴|a n |＝??
? 7－2n ，n ≤3，2n －7，n ≥4，
①当n ≤3时，S n ＝－(a 1＋a 2＋…＋a n )＝5＋(7－2n )
2n ＝6n －n 2
； ②当n ≥4时，S n ＝－a 1－a 2－a 3＋a 4＋…＋a n ＝－2(a 1＋a 2＋a 3)＋(a 1＋a 2＋…＋a n )＝18－6n ＋n 2.
综上，数列{|a n |}的前n 项和S n ＝??
?
－n 2＋6n ，n ≤3，n 2－6n ＋18，n ≥4.
11．(2020·广西南宁调研)已知正项数列{a n }的前n 项和为S n ，a 1＝1，S 2
n ＝a 2n ＋1－λS n ＋1，其中λ为常数．
(1)证明：S n ＋1＝2S n ＋λ；
(2)是否存在实数λ，使得数列{a n }为等比数列？若存在，求出λ；若不存在，请说明理由．
[解] (1)证明：∵a n ＋1＝S n ＋1－S n ，S 2
n ＝a 2n ＋1－λS n ＋1， ∴S 2n ＝(S n ＋1－S n )2－λS n ＋1，
∴S n ＋1(S n ＋1－2S n －λ)＝0. ∵a n >0，∴S n ＋1>0，
∴S n ＋1－2S n －λ＝0，∴S n ＋1＝2S n ＋λ. (2)∵S n ＋1＝2S n ＋λ， ∴S n ＝2S n －1＋λ(n ≥2)，
两式相减，得a n ＋1＝2a n (n ≥2)． ∵S 2＝2S 1＋λ，即a 2＋a 1＝2a 1＋λ， ∴a 2＝1＋λ，由a 2>0，得λ>－1.
若{a n }是等比数列，则a 1a 3＝a 2
2，
即2(λ＋1)＝(λ＋1)2，得λ＝1. 经检验，λ＝1符合题意．
故存在λ＝1，使得数列{a n }为等比数列．
12．(2020·合肥质检)已知等差数列{a n }的前n 项和为S n ，a 2＝1，S 7＝14，数列{b n }满足b 1·b 2·b 3·…·b n ＝2
n 2＋n
2
.
(1)求数列{a n }和{b n }的通项公式；
(2)若数列{c n }满足c n ＝b n cos(a n π)，求数列{c n }的前2n 项和T 2n . [解] (1)设等差数列{a n }的公差为d ，由a 2＝1，S 7＝14，
得??
?
a 1＋d ＝1，7a 1＋21d ＝14.
解得a 1＝12，d ＝12，∴a n ＝n
2.
∵b 1·b 2·b 3·…·b n ＝2 n 2＋n 2 ＝2 n (n ＋1)2
， ∴b 1·b 2·b 3·…·b n －1＝2
n (n ＋1)
2
(n ≥2)，
两式相除得b n ＝2n (n ≥2)． 又当n ＝1时，b 1＝2也适合上式，
∴b n ＝2n .
(2)∵c n ＝b n cos(a n π)＝2n
cos ? ??
??
n 2π，
∴T 2n ＝2cos π2＋22cosπ＋23
cos 3π2＋24cos(2π)＋ (22)
－
1
cos (2n －1)π
2
＋22n
cos(n π) ＝22cosπ＋24cos(2π)＋26cos(3π)＋…＋22n cos(n π) ＝－22＋24－26＋…＋(－1)n ·22n ＝－4[1－(－4)n ]
1＋4
＝－4＋(－4)n ＋1
5
.
中考英语知识点复习 专题十四：简单句
中考英语知识点复习专题十四简单句 易错清单 一、陈述句的否定结构 1. 含有have的否定句 (1) have当“拥有,所有”讲时,其否定形式有两种。如: I have an e-dictionary. 我有一个电子词典。 可改为:I don't have an e-dictionary. (√) I have not an e-dictionary. (√) (2) have作“吃、喝、玩、度过”讲时,其否定形式借助于助动词do。如: I had milk for breakfast this morning. (变否定句) →I didn't have milk for breakfast this morning. (3) have为助动词时,其否定形式为haven't。如: I have visited Diaoyu Island. (变否定句) →I haven't visited Diaoyu Island. 2. 注意以下几种情况: (1)含有all, both, each, every, both...and...等的肯定句加not变为否定句后,只表示部分否定;若表示全部否定,则需分别用no, no one, nobody, none, neither, neither...nor...等词替换上述词。如: Both Mary and Joan are students →Neither Mary nor Joan is a student. (2)含有already (已经),too (也)的肯定句加not变为否定句时,要分别把already和too改为yet和either。如: He has already seen the movie. (变为否定句) →He hasn't seen the movie yet. I want to go for a picnic, too. (变否定句) →I don't want to go for a picnic,either. (3)含有almost, many, much, often等词的肯定句可直接用never (hardly),few, little, seldom 变为否定句,而不用加not。如: He always stays up late in the evening. (变为否定句) →He never (hardly) stays up late in the evening. There is much food in the fridge. (变为否定句)→There is little food in the fridge.
2020版中考英语大二轮语法突破安徽专用13. 专题十三 简单句
第二部分语法专题研究 专题十三简单句 备考精练 1. (2019北京)—Excuse me, ________ is this T-shirt? —It's 88 yuan. A. how much B. how many C. how long D. how old 2. (2019南京)—________ will the Jinniu Lake Animal Kingdom be open? —Maybe in the second half of this year. A. When B. Who C. What D. Where 3. (2019淮安)—Mr.Black, ________ will the parents' meeting last? —It's hard to say. Maybe one hour or more. A. how long B. how much C. how far D. how often 4. (2019宜昌)—More and more people prefer to walk rather than ride in cars. —________．Walking is good for health. A. So they are B. So are they C. So they do D. So do they 5. (2019鄂州) —Last summer holiday, I didn't go anywhere. How boring! —________. But I'm going somewhere for a holiday this summer. A. Neither I did B. Neither did I C. So did I D. So I did 6. (2019凉山州)________ nice weather it is! Let's go out for a picnic. A. What B. What a C. How D. How a 7. (2019怀化改编)—________ dictionary is this? It's very nice.
(课标版)云南省2018年中考英语总复习第二部分语法专题研究专题十三简单句试题
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湖南专版2020中考英语复习：语法专题突破专题十三简单句语法综合演练
专题(十三) 简单句语法综合演练 1.—Guess what? I took part in an interview on TV last Sunday. —Oh, unforgettable experience it must be! A.what B.what an C.how 2.[2019·长郡一模]—The weather report says it will be sunny tomorrow. —fine weather it will be! Let’s go hiking. A.What B.What a C.How 3.[2019·天水改编] exciting news it is! Beijing will hold 2022 Winter Olympic Games. A.What an B.What C.How 4.[2019·眉山改编] noise pollution, and we can live in a quiet environment. A.Prevent B.Preventing C.Prevented 5.[2019·天水改编]—There is nothing left in the fridge, ? —. Let’s go to the supermarket to buy some. A.is there; Yes B.isn’t there; Yes C.is there; No 6.[2019·眉山改编]—Dad, can we reach Huangguoshu Waterfall? —In about an hour. A.how long B.how soon C.how often 7.[2019·鄂州改编]—Last summer holiday, I didn’t go anywhere. How boring! —. But I’m going somewhere for a holiday this summer. A.Neither I did B.Neither did I C.So did I 8.— students are there in your class? —Fifty. A.How many B.How much C.How long 9.People in the past could hardly eat fresh vegetables in winter, ? A.could they B.couldn’t they C.could people
2015中考英语专题(13)简单句
2015中考专题（13）简单句 【解读中考】 【考点分布】1.陈述句 2.疑问句 3.祈使句 4.感叹句 【考点内容】掌握陈述句的肯定和否定形式，实现肯定句和否定句之间的灵活转换。熟悉一般疑问句、特殊疑问句、反意疑问句、和选择疑问句之间的句型转换。了 解祈使句的特点，使用祈使句进行建议、命令、请求和劝告。能够熟练使用 what 和how引导的感叹句。 【命题趋势】1.各类简单句的构成及用法 2.重点考查特殊疑问句、反意疑问句、祈使句和感叹句的使用 3.what 和how引导的感叹句的辨析 【考点分析】 从以上表格可以看出，云南近五年的考题对简单句类型的考查， 一是集中在疑问句的疑问词，主要考查同类或同义疑问词相互间的用法辨析。 二是考查祈使句，尤其是对动词原形和特殊祈使句的考查。 三是考查感叹句，单项填空题对感叹句的考查主要集中在感叹词what和how及不定冠词的有无。
虽然近几年单纯考查这种基础句型的题不是很多，但是在阅读中有时需借助于划分句子成分去理解。 在书面表达中，没有最基本的遣词造句的能力是不可能用地道的英语句子来表达清楚的。有关简单句知识点的考查，渗透到了中考试题的各种题型，特别是句子翻译、单项填空、书面表达等，更需要牢固掌握这些基础知识。 第一讲陈述句 一、陈述句讲解： 【陈述句定义】：用来陈述事实或观点的句子叫做陈述句，句末用句号。 【陈述句分类】：陈述句分为肯定句和否定句。 (1)陈述句肯定式的正常语序是主语在谓语前。 We’ll meet again tomorrow. 我们明天再见。 (2)陈述句否定式的结构 ①含有be动词，助动词have, will和情态动词的否定形式是将not放在这些词的后面。 The desk is not made of wood. The girl didn’t do housework at home. Fish can’t live without water. ②实义动词的否定形式要借助于助动词，并且将否定词not加在助动词的后面。 I didn’t find Chinese easily at first. 起初，我发现学中文不容易。 ③除not外，其他否定词(no/none/little/few/never/nobody/seldom/neither/nor/hardly 等) 也可以构成否定句。 She has no ability in that kind of work. I have never met a foreigner who speaks such perfect Chinese. Nobody is allowed to be late. I have nothing much to do. I had never seen such a good match before that day! 在那天以前，我从来没有看过这么精彩的比赛！ 【拓展】当陈述句的谓语动词是have,表示“有”时，改为否定句的方法是： (1)have + not + 其他You have not any books. (2)have + no +其他You have no books. (3)don’t /doesn’t/ didn’t + have + 其他。如果句中有some，要将some改为any. You don’t have any books. 【中考真题训练】 【2014四川达州】Emma does her homework every evening.(变为否定句) Emma her homework every evening. 【2014甘肃兰州】I really don’t know what I can do to help her out.(改为简单句) I really don’t know what to help her out. 【答案】1.doesn’t;do 2.to do
第二部分 语法专题突破 13专题十三 几个特殊的简单句
专题十三几个特殊的简单句 单项填空 1.—delicious food you served us tonight!Thank you very much! —I'm glad that you enjoyed it. (C) C.What D.What a A.How B.How a (D) 2.Look!Laura is getting the first place.fast runner she is! A.How B.What C.How a D.What a 3.—is it from your home to your school,Anna? —It's quite near,only five minutes' walk. (B) B.How far A.How many D.How soon C.How long 4.(2019·长春)clever dog Lucky is!It can understand Mr.Smith's orders. (B) A.What B.What a C.How D.How a (A) 5.Look,excited the boy is on seeing these cute pandas! A.how B.how an C.what an D.what m late. 6.—Sorry,I' )(—tell me the bus broke down again! C D.No C.DonB.Not 't A.Never to 7.carefully,Michael!There)(A's a school ahead. A.Drive B.To drive D.Driving C.Drove
课标版云南省2019年中考英语总复习第二部分语法专题研究专题十三简单句试题(含解析)18
专题十三简单句 1. (2018武汉)—Do you think I could borrow your pencil? —________. A. Yes, you may borrow B. Yes, you could C. Yes, go on D. Yes, help yourself 2. (2018梧州)—Most of us have all worked very hard over the last three years. —Yes. ________ unusual journey we have! A. How B. What C. How an D. What an 3. (2018西宁)—________ excellent work you have done! —It's very kind of you to say so. A. What B. How C. What an D. How an 4. (2018广东)—Is there any outdoor learning in your school? —________. We learn outdoors once or twice every month. A. Yes, there is B. No, there isn’t C. Yes, it is D. No, it isn’t 5. (2018黔南)There ________ an NBA match on TV this weekend. A. will play B. is going to be C. will have D. is going to have 6. (2018黔南)—Summy ate nothing for breakfast this morning, ________？—No, because she had a stomachache. A. isn’t she B. was she C. didn’t she D. did she 7. (2018宜昌)—People choose high-speed train or self-driving to travel on
2020中考英语复习第二篇语法专题突破语法专题训练13简单句试题
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13. 专题十三 句子种类及简单句
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2019中考专项复习专题专题十三简单句 （限时：25分钟分值：38分得分：_______) 1.（2017郴州）—_______ friendly boy he is! —Yes. He’s always ready to help others. A. What a B. What C. How 2.（2017绥化）—Your father went to the park yesterday, _______? —Yes, he did. A. didn’t he B. doesn’t he C. did he 3. （2017上海改编）—Do you know _______ a 5-day trip to Hong Kong costs? —I guess it’s about ￥4, 000. A. how fast B. how long C. how much 4. （2017连云港改编）—_______ do the students in your school do outdoor activities every day? —At least an hour. A. How often B. How long C. How much 5.（2017泰安改编）—_______ exciting the speech about “Belt and Road”was! —Of course! It was a really great inspiration to the world. A. How B. What C. How a 6.（2017南京改编）—Millie, _______ do you take the course in DIY? —Every Saturday afternoon. A. how long B. how far C. how often 7.（2017随州改编）—Is the mobile phone new or old? —________. I bought it only two days ago. A. It’s old B. It’s new C. Yes, it is 8.（2017重庆B卷改编）________ bad day! It’s raining hard. We have to stay at home.
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