必修5——5作业
2020年高中数学 人教A版 必修5 课后作业本《等比数列的概念和通项公式》(含答案解析)
2020年高中数学 人教A 版 必修5 课后作业本《等比数列的概念和通项公式》一、选择题1.已知等比数列{a n }中，a 1=32，公比q=-12，则a 6等于( )A ．1B ．-1C ．2 D.122.已知数列a ，a(1-a)，a(1-a)2，…是等比数列，则实数a 的取值范围是( )A ．a≠1B ．a≠0且a≠1C ．a≠0D ．a≠0或a≠13.在等比数列{a n }中，a 2 016=8a 2 013，则公比q 的值为( )A ．2B ．3C ．4D ．84.已知等比数列{a n }满足a 1＋a 2=3，a 2＋a 3=6，则a 7等于( )A ．64B ．81C ．128D ．2435.等比数列{a n }各项均为正数，且a 1，12a 3，a 2成等差数列，则a 3＋a 4a 4＋a 5=( )A ．-5＋12 B.1－52 C.5－12 D ．-5＋12或5－126.设{a n }是由正数组成的等比数列，公比q=2，且a 1·a 2·a 3·…·a 30=230，那么a 3·a 6·a 9·…·a 30等于( )A ．210B ．220C ．216D ．2157.已知等比数列{a n }满足a 1=3，a 1＋a 3＋a 5=21，则a 3＋a 5＋a 7=( )A ．21B ．42C ．63D ．84二、填空题8.首项为3的等比数列的第n 项是48，第2n-3项是192，则n=________.9.数列{a n }为等比数列，a n >0，若a 1·a 5=16，a 4=8，则a n =________.10.若k,2k ＋2,3k ＋3是等比数列的前3项，则第四项为________．11.设{a n }为公比q>1的等比数列，若a 2 014和a 2 015是方程4x 2-8x ＋3=0的两根， 则a 2 016＋a 2 017=________.12.在正项等比数列{a n }中，已知a 1a 2a 3=4，a 4a 5a 6=12，a n-1a n a n ＋1=324，则n=________.三、解答题13.已知数列{a n }的前n 项和S n =2a n ＋1，求证：{a n }是等比数列，并求出通项公式．14.在各项均为负的等比数列{a n }中，2a n =3a n ＋1，且a 2·a 5=827.(1)求数列{a n }的通项公式；(2)-1681是否为该数列的项？若是，为第几项？15.有四个实数，前三个数依次成等比数列，它们的积为-8；后三个数依次成等差数列，它们的积为-80，求这四个数．16.已知a1=2，点(a n，a n＋1)在函数f(x)=x2＋2x的图象上，其中n=1,2,3，….(1)证明数列{lg(1＋a n)}是等比数列；(2)求{a n}的通项公式．答案解析1.答案为：B ；解析：由题知a 6=a 1q 5=32×⎝ ⎛⎭⎪⎫－125=-1，故选B.2.答案为：B ；解析：由a 1≠0，q≠0，得a≠0,1-a≠0，所以a≠0且a≠1.3.答案为：A ；解析：q 3=a 2 016a 2 013=8，∴q=2.4.答案为：A ；解析：∵{a n }为等比数列，∴a 2＋a 3a 1＋a 2=q=2.又a 1＋a 2=3，∴a 1=1.故a 7=1×26=64.5.答案为：C ；解析：a 1，12a 3，a 2成等差数列，所以a 3=a 1＋a 2，从而q 2=1＋q ，∵q>0，∴q=5＋12，∴a 3＋a 4a 4＋a 5=1q =5－12.6.答案为：B ；解析：由等比数列的定义，a 1·a 2·a 3=⎝ ⎛⎭⎪⎫a 3q 3，故a 1·a 2·a 3·…·a 30=⎝ ⎛⎭⎪⎫a 3·a 6·a 9·…·a 30q 103.又q=2，故a 3·a 6·a 9·…·a 30=220.7.答案为：B ；解析：设等比数列公比为q ，则a 1＋a 1q 2＋a 1q 4=21，又因为a 1=3，所以q 4＋q 2-6=0，解得q 2=2，所以a 3＋a 5＋a 7=(a 1＋a 3＋a 5)q 2=42.8.答案为：5；解析：设公比为q ，则⎩⎪⎨⎪⎧ 3q n －1＝483q 2n －4＝192⇒⎩⎪⎨⎪⎧q n －1＝16q 2n －4＝64⇒q 2=4，得q=±2.由(±2)n-1=16，得n=5.9.答案为：2n-1解析：由a 1·a 5=16，a 4=8，得a 21q 4=16，a 1q 3=8，所以q 2=4，又a n >0，故q=2，a 1=1，a n =2n-1.10.答案为：- 272；解析：由题意，(2k ＋2)2=k(3k ＋3)，解得k=-4或k=-1， 又k=-1时，2k ＋2=3k ＋3=0，不符合等比数列的定义，所以k=-4，前3项为-4，-6，-9，第四项为-272.11.答案为：18；解析：4x 2-8x ＋3=0的两根分别为12和32，q>1，从而a 2 014=12，a 2 015=32，∴q=a 2 015a 2 014=3.a 2 016＋a 2 017=(a 2 014＋a 2 015)·q 2=2×32=18.12.答案为：14；解析：设数列{a n }的公比为q ，由a 1a 2a 3=4=a 31q 3与a 4a 5a 6=12=a 31q 12可得q 9=3，又a n-1a n a n ＋1=a 31q 3n-3=324，因此q 3n-6=81=34=q 36，所以n=14.13.证明：∵S n =2a n ＋1，∴S n ＋1=2a n ＋1＋1.∴S n ＋1-S n =a n ＋1=(2a n ＋1＋1)-(2a n ＋1)=2a n ＋1-2a n . ∴a n ＋1=2a n .①又∵S 1=a 1=2a 1＋1， ∴a 1=-1≠0.由①式可知，a n ≠0，∴由a n ＋1a n=2知{a n }是等比数列，a n =-2n-1.14.解：(1)∵2a n =3a n ＋1，∴a n ＋1a n =23，数列{a n }是公比为23的等比数列，又a 2·a 5=827，所以a 21⎝ ⎛⎭⎪⎫235=⎝ ⎛⎭⎪⎫233，由于各项均为负，故a 1=-32，a n =-⎝ ⎛⎭⎪⎫23n-2.(2)设a n =-1681，则-1681=-⎝ ⎛⎭⎪⎫23n-2，⎝ ⎛⎭⎪⎫23n-2=⎝ ⎛⎭⎪⎫234，n=6，所以-1681是该数列的项，为第6项．15.解：由题意，设这四个数为bq，b ，bq ，a ，则⎩⎪⎨⎪⎧b 3＝－8.2bq ＝a ＋b ，b 2aq ＝－80解得⎩⎪⎨⎪⎧a ＝10，b ＝－2，q ＝－2，或⎩⎪⎨⎪⎧a ＝－8，b ＝－2，q ＝52.∴这四个数依次为1，-2,4,10或-45，-2，-5，-8.16.解：(1)证明：由已知得a n ＋1=a 2n ＋2a n ，∴a n ＋1＋1=a 2n ＋2a n ＋1=(a n ＋1)2.∵a 1=2，∴a n ＋1＋1=(a n ＋1)2>0.∴lg(1＋a n ＋1)=2lg(1＋a n )，即lg 1＋a n ＋1lg 1＋a n=2，且lg(1＋a 1)=lg 3.∴{lg(1＋a n )}是首项为lg 3，公比为2的等比数列． (2)由(1)知，lg(1＋a n )=2n-1·lg 3=lg 312n －，∴1＋a n =312n －，∴a n =312n －-1.。
2020年高中数学 人教A版 必修5 课后作业本《等差数列的前n项和公式》(含答案解析)
2020年高中数学 人教A 版 必修5 课后作业本《等差数列的前n 项和公式》一、选择题1.等差数列{a n }中，d=2，a n =11，S n =35，则a 1等于( )A ．5或7B ．3或5C ．7或-1D ．3或-12.已知等差数列{a n }的前n 项和为S n ，若S 2=4，S 4=20，则该数列的公差d 为( )A ．7B ．6C ．3D ．23.已知等差数列{a n }满足a 2＋a 4=4，a 3＋a 5=10，则它的前10项的和S 10等于( )A ．138B ．135C ．95D ．234.若等差数列{a n }的前5项和S 5=25，且a 2=3，则a 7等于( )A ．12B ．13C ．14D ．155.已知数列{a n }的前n 项和S n =n 2-9n ，第k 项满足5＜a k ＜8，则k 等于( )A ．9B ．8C ．7D ．66.S n 是等差数列{a n }的前n 项和，a 3＋a 6＋a 12为一个常数，则下列也是常数的是( )A ．S 17 B ．S 15 C ．S 13 D ．S 77.设等差数列{a n }的前n 项和为S n ，S m-1=-2，S m =0，S m ＋1=3，则m=( )A ．3B ．4C ．5D ．6二、填空题8.已知数列{a n }中，a 1=1，a n =a n-1＋(n≥2)，则数列{a n }的前9项和等于________．129.等差数列{a n }中，若a 10=10，a 19=100，前n 项和S n =0，则n=________.10.等差数列{a n }中，a 2＋a 7＋a 12=24，则S 13=________.11.设S n 是等差数列{a n }的前n 项和，若=，则等于________．a5a359S9S512.设等差数列{a n}的前n项和为S n，已知前6项和为36，最后6项和为180，S n=324(n>6)，则数列的项数n=________，a9＋a10=________.三、解答题13.在等差数列{a n}中：(1)已知a5＋a10=58，a4＋a9=50，求S10；(2)已知S7=42，S n=510，a n-3=45，求n.14.在等差数列{a n}中，a10=18，前5项的和S5=-15，(1)求数列{a n}的通项公式；(2)求数列{a n}的前n项和的最小值，并指出何时取得最小值．15.等差数列{a n }的前n 项和S n =-n 2＋n ，求数列{|a n |}的前n 项和T n .32205216.设{a n }为等差数列，S n 为数列{a n }的前n 项和，已知S 7=7，S 15=75，T n 为数列的前n 项{Sn n}和，求T n .答案解析1.答案为：D ；解析：由题意，得Error!即Error!解得Error!或Error!2.答案为：C ；解析：由S 2=4，S 4=20，得2a 1＋d=4,4a 1＋6d=20，解得d=3.3.答案为：C ；解析：由a 2＋a 4=4，a 3＋a 5=10，可知d=3，a 1=-4.∴S 10=-40＋×3=95.10×924.答案为：B ；解析：由S 5=5a 3=25，∴a 3=5.∴d=a 3-a 2=5-3=2.∴a 7=a 2＋5d=3＋10=13.5.答案为：B ；解析：当n=1时，a 1=S 1=-8；当n≥2时，a n =S n -S n-1=(n 2-9n)-[(n-1) 2-9(n-1)]=2n-10.综上可得数列{a n }的通项公式a n =2n-10.所以a k =2k-10.令5＜2k-10＜8，解得k=8.6.答案为：C ；解析：∵a 3＋a 6＋a 12为常数，∴a 2＋a 7＋a 12=3a 7为常数，∴a 7为常数．又S 13=13a 7，∴S 13为常数．7.答案为：C ；解析：a m =S m -S m-1=2，a m ＋1=S m ＋1-S m =3，∴d=a m ＋1-a m =1，由S m ==0，知a 1=-a m =-2，a m =-2＋(m-1)=2，解得m=5. a1＋am m 28.答案为：27；解析：∵n≥2时，a n =a n-1＋，且a 1=1，所以数列{a n }是以1为首项，12以为公差的等差数列，所以S 9=9×1＋×=9＋18=27.129×82129.答案为：17；解析：Error!，∴d=10，a 1=-80.∴S n =-80n ＋×10=0，n n －1 2∴-80n ＋5n(n-1)=0，n=17.10.答案为：104；解析：因为a 1＋a 13=a 2＋a 12=2a 7，又a 2＋a 7＋a 12=24，所以a 7=8.所以S 13==13×8=104.13 a1＋a13 211.答案为：1；解析：由等差数列的性质，===，∴==×=1.a5a32a52a3a1＋a9a1＋a559S9S592 a1＋a9 52a1＋a5 955912.答案为：18，36；解析：由题意，可知a 1＋a 2＋…＋a 6=36 ①，a n ＋a n-1＋a n-2＋…＋a n-5=180 ②，由①＋②，得(a 1＋a n )＋(a 2＋a n-1)＋…＋(a 6＋a n-5)=6(a 1＋a n )=216，∴a 1＋a n =36.又S n ==324，∴18n=324，∴n=18，∴a 1＋a 18=36，∴a 9＋a 10=a 1＋a 18=36.n a1＋an 213.解：(1)由已知条件得Error!解得Error!∴S 10=10a 1＋d=10×3＋×4=210.10× 10－1 210×92(2)S 7==7a 4=42，7 a1＋a7 2∴a 4=6.∴S n ====510.n a1＋an 2n a4＋an －3 2n 6＋45 2∴n=20.14.解：(1)设{a n }的首项，公差分别为a 1，d.则Error!解得a 1=-9，d=3，∴a n =3n-12.(2)S n ==(3n 2-21n)=2-，n a1＋an 21232(n －72)1478∴当n=3或4时，前n 项的和取得最小值为-18.15.解：a 1=S 1=101，当n≥2时，a n =S n -S n-1=-n 2＋n-Error!Error!=-3n ＋104，a 1=S 1=101也适合上式，322052所以a n =-3n ＋104，令a n =0，n=34，故n≥35时，a n <0，n≤34时，a n >0，23所以对数列{|a n |}，n≤34时，T n =|a 1|＋|a 2|＋…＋|a n |=a 1＋a 2＋…＋a n =-n 2＋n ，322052当n≥35时，T n =|a 1|＋|a 2|＋…＋|a 34|＋|a 35|＋…＋|a n |=a 1＋a 2＋…＋a 34-a 35-…-a n=2(a 1＋a 2＋…＋a 34)-(a 1＋a 2＋…＋a n )=2S 34-S n =n 2-n ＋3 502，322052所以T n =Error!16.解：设等差数列{a n }的公差为d ，则S n =na 1＋n(n-1)d ，12∵S 7=7，S 15=75，∴Error!即Error!解得Error!∴=a 1＋(n-1)d=-2＋(n-1)，Sn n 1212∵-=，Sn ＋1n ＋1Sn n 12∴数列是等差数列，其首项为-2，公差为，{Sn n }12∴T n =n×(-2)＋×=n 2-n.n· n －1 2121494。
人教版高中英语必修5课时分层作业：unit1课时分层作业2 Section Ⅱ【含答案】
课时分层作业(二)Section Ⅱ(建议用时：40分钟)[语言知识练习固基础]Ⅰ.单句语法填空1．The two astronauts will carry out a series of scientific(science) experiments in spaceship.2．What conclusion do you draw from the research?3．The suggestion he had put forward was turned down at the meeting.4．When I opened the door，I found my father sitting in his chair，completely absorbed in the newspaper.5．His son is very naughty and has formed some bad habits.I think he should cure him of them.6．The concern of this book is with air pollution (pollute)．7．Please read the instructions (instruct) carefully before using it.8．The talks are continuing，but no announcements(announce) are expected at this time.9．The incident exposed (expose) the weakness of the school's position.10．We consider that you are to blame(blame) for the accident.Ⅱ.完成句子1．从这些事实中我得出他很努力这一结论。
2020年高中数学 人教A版 必修5 同步作业本《等差数列的性质》(含答案解析)
2020年高中数学 人教A 版 必修5 同步作业本《等差数列的性质》一、选择题1.设数列{a n }，{b n }都是等差数列，且a 1=25，b 1=75，a 2＋b 2=100，那么由a n ＋b n 所组成的数列的第37项值为( )A ．0B ．37C ．100D ．-372.如果数列{a n }是等差数列，则下列式子一定成立的有( )A ．a 1＋a 8＜a 4＋a 5B ．a 1＋a 8=a 4＋a 5C ．a 1＋a 8＞a 4＋a 5D ．a 1a 8=a 4a 53.由公差d≠0的等差数列a 1，a 2，…，a n 组成一个新的数列a 1＋a 3，a 2＋a 4，a 3＋a 5，…下列说法正确的是( )A ．新数列不是等差数列B ．新数列是公差为d 的等差数列C ．新数列是公差为2d 的等差数列D ．新数列是公差为3d 的等差数列4.在数列{a n }中，a 3=2，a 7=1，如果数列是等差数列，那么a 11等于( ){1an ＋1}A. B. C. D ．11312235.一个首项为23，公差为整数的等差数列，如果前六项均为正数，第七项起为负数，则它的公差是( )A ．-2B ．-3C ．-4D ．-56.若方程(x 2-2x ＋m)(x 2-2x ＋n)=0的四个根组成一个首项为的等差数列，则|m-n|=( )14A ．1 B. C. D.341238二、填空题7.在等差数列{a n }中，a 3，a 10是方程x 2-3x-5=0的根，则a 5＋a 8=________．8.数列{a n }满足递推关系a n =3a n-1＋3n -1(n∈N *，n ≥2)，a 1=5，则使得数列为等差数列{an ＋m 3n }的实数m 的值为________．9.已知数列{a n }满足a 1=1，若点在直线x-y ＋1=0上，则a n =___________．(an n ，an ＋1n ＋1)10.若数列{a n }为等差数列，a p =q ，a q =p(p≠q)，则a p ＋q =______________．三、解答题11.在等差数列{a n }中，若a 1＋a 2＋…＋a 5=30，a 6＋a 7＋…＋a 10=80，求a 11＋a 12＋…＋a 15.12.已知无穷等差数列{a n }，首项a 1=3，公差d=-5，依次取出项的序号被4除余3的项组成数列{b n }．(1)求b 1和b 2；(2)求数列{b n }的通项公式；(3)数列{b n }中的第110项是数列{a n }中的第几项？13.在数列{a n }中，a 1=1，3a n a n-1＋a n -a n-1=0(n≥2，n ∈N *)．(1)求证：数列是等差数列；{1an}(2)求数列{a n }的通项公式．答案解析1.答案为：C ；解析：设c n =a n ＋b n ，则c 1=a 1＋b 1=25＋75=100，c 2=a 2＋b 2=100，故d=c 2-c 1=0，故c n =100(n∈N *)，从而c 37=100.2.答案为：B ；解析：由等差数列的性质有a 1＋a 8=a 4＋a 5.3.答案为：C ；解析：因为(a n ＋1＋a n ＋3)-(a n ＋a n ＋2)=(a n ＋1＋a n )＋(a n ＋3-a n ＋2)=2d ，所以数列a 1＋a 3，a 2＋a 4，a 3＋a 5，…是公差为2d 的等差数列．4.答案为：B ；解析：依题意得＋=2·，所以=-=，所以a 11=.1a3＋11a11＋11a7＋11a11＋121＋112＋123125.答案为：C ；解析：设该数列的公差为d ，则由题设条件知：a 6=a 1＋5d>0，a 7=a 1＋6d<0.又因为a 1=23，所以即-<d<-，又因为d 是整数，所以d=-4.{d >－235，d <－236，)2352366.答案为：C ；解析：设方程的四个根a 1，a 2，a 3，a 4依次成等差数列，则a 1＋a 4=a 2＋a 3=2，再设此等差数列的公差为d ，则2a 1＋3d=2，因为a 1=，所以d=，所以a 2=＋=，a 3=＋1=，a 4=＋=，14121412341454143274所以|m-n|=|a 1a 4-a 2a 3|==.|14×74－34×54|127.答案为：3；解析：由已知得a 3＋a 10=3.又数列{a n }为等差数列，所以a 5＋a 8=a 3＋a 10=3.8.答案为：- ；12解析：a 1=5，a 2=3×5＋32-1=23，a 3=3×23＋33-1=95，依题意得，，成等差数列，所以2·=＋，所以m=-.5＋m 323＋m 3295＋m 3323＋m 325＋m 395＋m 33129.答案为：n 2解析：由题设可得-＋1=0，即-=1，所以数列是以1为公差的等差数an n an ＋1n ＋1an ＋1n ＋1an n {an n}列，且首项为1，故通项公式=n ，所以a n =n 2.an n 10.答案为：0；解析：法一：因为a p =a q ＋(p-q)d ，所以q=p ＋(p-q)d ，即q-p=(p-q)d ，因为p≠q，所以d=-1.所以a p ＋q =a p ＋(p ＋q-p)d=q ＋q×(-1)=0.法二：因为数列{a n }为等差数列，所以点(n ，a n )在一条直线上．不妨设p ＜q ，记点A(p ，q)，B(q ，p)，则直线AB 的斜率k==-1，如图所示，由图知OC=p ＋q ，即点C 的坐标为(p ＋q ，0)故a p ＋q =0.p －q q －p11.解：法一：因为1＋11=6＋6，2＋12=7＋7，…，5＋15=10＋10，所以a 1＋a 11=2a 6，a 2＋a 12=2a 7，…，a 5＋a 15=2a 10.所以(a 1＋a 2＋…＋a 5)＋(a 11＋a 12＋…＋a 15)=2(a 6＋a 7＋…＋a 10)．所以a 11＋a 12＋…＋a 15=2(a 6＋a 7＋…＋a 10)-(a 1＋a 2＋…＋a 5)=2×80-30=130.法二：因为数列{a n }是等差数列，所以a 1＋a 2＋…＋a 5，a 6＋a 7＋…＋a 10，a 11＋a 12＋…＋a 15也成等差数列，即30，80，a 11＋a 12＋…＋a 15成等差数列．所以30＋(a 11＋a 12＋…＋a 15)=2×80，所以a 11＋a 12＋…＋a 15=130.12.解：(1)由题意，等差数列{a n }的通项公式为a n =3＋(n-1)(-5)=8-5n ，设数列{b n }的第n 项是数列{a n }的第m 项，则需满足m=4n-1，n ∈N *，所以b 1=a 3=8-5×3=-7，b 2=a 7=8-5×7=-27.(2)由(1)知b n ＋1-b n =a 4(n ＋1)-1-a 4n-1=4d=-20，所以新数列{b n }也为等差数列，且首项为b 1=-7，公差为d′=-20，所以b n =b 1＋(n-1)d′=-7＋(n-1)×(-20)=13-20n.(3)因为m=4n-1，n ∈N *，所以当n=110时，m=4×110-1=439，所以数列{b n }中的第110项是数列{a n }中的第439项．13. (1)证明：由3a n a n-1＋a n -a n-1=0，得-=3(n≥2)．1an 1an －1又因为a 1=1，所以数列是以1为首项，3为公差的等差数列．{1an}(2)解：由(1)可得=1＋3(n-1)=3n-2，所以a n =.1an 13n －2又当n=1时，a 1=1，符合上式，所以数列{a n }的通项公式是a n =.13n －2。
2020高考英语新创新大一轮复习人教全国版精练必修5Unit5课下作业(一_三)含答案
必修5 Unit 5 课下作业（一~三）课下作业（一）考点过关针对练Ⅰ.单词拼写1．Cut the lemon in half and squeeze (榨；挤) the juice out into the bowl.2．These men made themselves famous for their courage and bravery (勇敢)．3．They have earned lots of money, so I firmly (坚定地) believe that the business is a success.4．The heavy stress from the study was unbearable (难以忍受的), so Li Lin got depressed and decided to give up.5．The skin, whose functions are very complex, is our body's largest organ which acts as a barrier (屏障) against disease and the sun's harmful rays.6．One of the station staff saw he was in difficulty and came to his aid (援助)．7．The moment he graduated from college, he applied (申请) to be sent to the northwest of China.8．The difficulty is temporary (暂时的)．Once it's overcome, the project will go smoothly.9．Nowadays the purpose of school is to treat (对待) every student as an individual and to motivate them to reach their potential.10．The doctor said that my eyes would be a little swollen (肿胀的), so I needed to rest at home for a few days.Ⅱ.语境语法填空1．As is known to us, it is vital ❶to_know (know) some knowledge of first aid as danger lies everywhere and accidents happen from time to time.For example, we can get ❷cut (cut) by a ❸variety (various) of things.When your hand bleeds, treat it in time.If the cut is not serious, press it ❹firmly (firm) and soon it will stop ❺bleeding (bleed)．If the cut is deep, first tie a bandage around it and then ask a doctor to apply some medicine ❻to it.2．One day, Tom was driving his car to his company ❶when he saw a girl injured in a traffic accident. To make matters worse, the girl was bleeding.Jumping out of the car, Tom gave her first aid and then put her ❷in place, waiting for the ambulance. As a result, his knowledge of first aid made a ❸difference (differ) to the girl.3．One day Mike ❶was_studying (study) in his room when he heard a scream from the kitchen. He rushed out and found his mother got burned while ❷cooking (cook). Mike remembered what he had learned at school. First, he took off the clothes that his mother was wearing near the burns. Then, he put clean cloth in the cold water, ❸squeezed (squeeze) water out and placed it on the burned area over ❹and over again until the pain was not so bad. At last, he put his hands ❺on a dry and clean bandage and went to a doctor with his mother.Ⅲ.语境改错1．文中共有5处错误，每句中最多有两处，请找出并改正。
外研版高二英语必修5_好题精练：Module2_课时小作业
Module2 课时小作业Ⅰ.语音知识1．standardA．|′stəndaːd|B．|′stændəd|C．|stændaːd| D．|′staːndəd|2．compareA．|kəm′pɛə| B．|kəm′peə|C．|kʌm′pɛə| D．|kʌm′peə|3．switchA．|′swik| B．|′swa itʃ|C．|′swiːtʃ| D．|′switʃ|4．volunteerA．|′ vɔlən′tiə| B．|vʌlən′tiə|C．|vʌluːn′t iə| D．|vɔlən′tiː|5．combinationA．|kɔm′bi′ neiʃn| B．|′kɔmbi′ neiʃn|C．|′ kɔmbi′neiʃn| D．|′ kɔmbinei′ʃn|Ⅱ.情景对话—Hello.I’m calling about the apartment you advertised.—Yes.__1__—I’m interest ed in a one-bedroom apartment.Do you have any available? —__2__When do you need it?—Sometime around next week.What can you tell me about this apartment? —__3__The monthly rent is $650，with a $300 security deposit.—__4__May I come over tomorrow to take a look?—Sure.What time would you like to come?—__5__—Good.May I have your name，please?—My name is Blanca.—Blanca.I’ll see you tomorrow.A．No，I have another oneB．Well，it’s a onebedroom apartment.C．It’s kind of youD．How about 10 a．m.?E．Yes.I have one.F．What kinds of apartments do you prefer?G．Sounds good.Ⅲ.单项填空1．—I want a room for ten people to have a get-together.—Luckily there is one________.A．available B．qualifiedC．standard D．impressive2．The trade union intended to call on the workers to go on strike________the government’s limitation on exports.A．in memory of B．in honour ofC．in response to D．in need of3．The agent was about to sign his name to the document_____________，to our surprise，a stranger broke in to prevent him.A．while B．whenC．as D．until4．The air is badly polluted because some factories don’t__________the rules to protect the environment.A．appreciate B．regardC．honour D．respect5．Much notice has been________the problems with the home-staying children in China.A．paid to B．kept onC．taken of D．made up6．I took it for________that he would try to help me out of the difficulty，but he didn’t at all.A．sure B．certainC．granted D．possible7．(2009年江苏锡山模拟)Please leave your phone number______we can get intouch with you in case of emergency.A．so that B．on condition thatC．for fear that D．so long as8．—Do you think our team will beat theirs?—Our team have better players，so I ________our team will win.A．want B．preferC．wish D．expect9．On a________cold win ter morning，his________body was found in a lonely forest.A．frozen；freezing B．freezing；frozenC．frozen；frozen D．freezing；freezing10．After he retired from office，Rogers________painting for a while，but soon lost interest.A．took up B．saved upC．kept up D．drew up11．The headteacher，________with what the student said，nodded with a smile. A．tiring B．tiredC．satisfying D．satisfied12．The shopowner would sell the MP4 for 800 yuan，but my elder brother________only 600 yuan.A．asked B．chargedC．sold D．offered13．Your suggestion sounds fine________，but would it work________？A．in practice；in theory B．in theory；in practiceC．in advance；in theory D．in general；in practice14．We have seen that method________some other conditions and it does work. A．applied to B．applying forC．applies to D．apply for15．(2009年泰安模拟) Only those who have the patience to do simple things perfectly will________the skill to do difficult things easily.A．demand B．acquireC．accomplish D．achieveⅣ.阅读理解A(2010年郑州第一次检测) Willa Cather once said，“When people ask me whether writing has been a hard or easy road，I always answer with the famous saying: The end is nothing；the road is all.That is what I mean when I say writing has been a pleasure.I have never used the computer with the thought that one more task had to be done.”Like most writers，Willa Cather did n ot write books for the money that they brought her，but rather for the pleasure that came in their writing.Her works were，like her，simple and full of the vigor of her days in Nebraska，where she grew from child to young womanhood and where she developed a deep love for the treeless land of the great plain with its wild flowers，wheat fields and rivers.“It’s a rather strange thing about the flat country，” she wrote later.“It takes hold of you or it leaves you perfectly cold.A great many people find it very dull；they like a church tower，an old factory，a waterfall，the country all made to look like a German Christmas card ...But when I come to the open plain，something happens.I’ m home.I breathe differently.”1．Willa Cather wrote because she found writing________.A．simple and livelyB．opened up a road to successC．neither too hard nor too easyD．interesting and enjoyable2．What was the place like where Cather grew up?A．It was cold，plain and without a church.B．It was vast，open and flat.C．It was like a German Christmas card.D．It was a colorful world of wild flowers.3．When she said “It takes hold of you or it leaves you perfectly cold.”，Willa Cather meant that________.A．you either love the place or hate itB．you decide either to stay or to leaveC．some find the place warm；others find it coldD．some find the place peaceful；others find it wild4．What happens when Cather comes to the open plain?A．She breathes differently from others.B．She wants to make the place her home.C．She feels completely comfortable.D．She finds the place similar to her home.B(2010年福建四地六校联考) Every country tends to accept its own way of life as being the normal one and to praise or criticize others，as they are similar to or different from it.And unfortunately，our picture of the people and the way of life of other countries is often a distorted (扭曲的) one.Here is a great argument in favor of foreign travel and learning foreign languages.It is only by traveling in a country and getting to know its inhabitants and their language that one can find out what a coun try and its people are really like.And how different the knowledge one gains this way frequently turns out to be from the second-hand information gathered from other sources! How often we find that the foreigners whom we thought to be such different people from ourselves are not very different at all!Differences between peoples do，of course，exist and，one hopes，will always continue to do so.The world will be a dull place indeed when all the different nationalities behave exactly alike，and some people might say that we are rapidly approaching this state of affairs.With the much greater rapidity (快速) and ease of travel，there might seem to be some truth in this at least as far as Europe is concerned.However this may be，at least the greater ease of travel today has revealed (展示) to more people than ever before that the Englishman or Frenchman or German is not：some different kind of animal from themselves.5．Every country criticizes ways of life in other countries becau se they are_____.A．distorted B．normalC．similar to each other D．different from its own6．One who travels in a foreign country and learns its language will________. A．find out why its people are differentB．argue in favor of this country and the languageC．know the country and its people betterD．like its inhabitants and their language7．The knowledge one gains by traveling in a foreign country is often________. A．from second-hand informationB．gathered from other sources rather than its inhabitantsC．gained from the arguments about the countryD．different from what one had before the travel8．In this passage，th e author wants to say________.A．differences between peoples will gradually disappear because of the ease of travelB．differences between peoples do exist even though different nationalities behave exactly alikeC．differences between peoples will continue to exist and the world will be a dull placeD．differences between peoples will not exist as one hopes参考答案Ⅰ.语音知识1．B 2.B 3.D 4.A 5.CⅡ.情景对话1．F 2.E 3.B 4.G 5.DⅢ.单项填空1．A available可利用的，常跟在修饰词的后面；其他三项“qualified合格的；standard标准的；impressive印象深刻的”作定语常放在修饰词之前，且与题意不符。
人教版高中历史必修上册精品课件 分层作业 第5课 三国两晋南北朝的政权更迭与民族交融
5.东晋南朝时期,南方土地大量开垦,农作物品种增加,产量提高;纺织、陶 瓷、造船等行业也有明显的进步。出现这一现象的主要原因是( A ) A.北方人口大量南迁 B.大批水利工程的兴建 C.江南自然资源丰富 D.政府重视经济的发展 解析 从西晋末年起,北方人民为躲避战乱,大批流亡南下,带来了先进的生 产工具和技术,也充实了劳动力资源,所以出现了“东晋南朝时期,南方土地 大量开垦”等现象,故选A项。
B.中央机构权力失衡
C.门阀士族逐渐衰落
D.中书权力制约皇权
解析 据材料信息可知,中书省的权力集中在庶人手中,士族阶层掌握的都
是“清贵华重”的职务,说明当时的实权掌握在庶族手中,士族逐渐边缘化,C
项正确。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
4.南北朝时期,形成了记述家族世系的谱学,“有司选举,必稽谱籍,而考其真
8.《资治通鉴》记述某一诏令“北人谓土为拓,后为跋。魏之先出于黄帝,
以土德王,故为拓跋氏。夫土者,黄中之色,万物之元也;宜改姓元氏。诸功
臣旧族自代来者,姓或重复,皆改之”。以上史料所反映的历史事件是( C )
A.楚国的吴起变法
B.秦国的商鞅变法
C.北魏孝文帝改革
D.北宋王安石变法
解析 材料中体现了北魏孝文帝改革中改汉姓,将拓跋姓改为元姓,故选C项。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12.据《宋书》记载,刘宋时期“荆城跨南楚之富,扬部有全吴之沃,鱼盐杞梓
之利,充仞八方,丝绵布帛之饶,覆衣天下”。这表明当时( C )
A.北方人民大量南迁
B.南方商业更加发达
2020年高中数学 人教A版 必修5 课后作业本《等比数列的前n项和公式》(含答案解析)
2020年高中数学 人教A 版 必修5 课后作业本《等比数列的前n 项和公式》一、选择题1.等比数列{a n }中，a n =2n ，则它的前n 项和S n =( )A ．2n -1B ．2n -2C ．2n ＋1-1D ．2n ＋1-22.在等比数列{a n }中，若a 1=1，a 4=，则该数列的前10项和S 10=( )18A ．2-B ．2-C ．2-D ．2-128129121012113.等比数列{a n }中，已知前4项之和为1，前8项和为17，则此等比数列的公比q 为( )A ．2 B ．-2 C ．2或-2 D ．2或-14.已知数列{a n }为等比数列，S n 是它的前n 项和，若a 2·a 3=2a 1，且a 4与2a 7的等差中项为，54则S 5=( )A ．35B ．33C ．31D ．295.等比数列{a n }中，a 3=3S 2＋2，a 4=3S 3＋2，则公比q 等于( )A ．2 B. C ．4 D.12146.已知等比数列{a n }的前n 项和S n =2n -1，则a ＋a ＋…＋a 等于( )2122n A ．(2n-1)2 B.(2n -1) C ．4n -1 D.(4n -1)13137.设S n 是等比数列{a n }的前n 项和，若=3，则=( )S4S2S6S4A ．2 B. C. D ．1或273310二、填空题8.若数列{a n }满足a 1=1，a n ＋1=2a n ，n=1,2,3，…，则a 1＋a 2＋…＋a n =________.9.等比数列{a n }的前n 项和为S n ，已知S 1,2S 2,3S 3成等差数列，则{a n }的公比为________．10.等比数列的前n 项和S n =m·3n ＋2，则m=________.11.已知数列{a n}是递增的等比数列，a1＋a4=9，a2a3=8，则数列{a n}的前n项和等于________．12.设数列{a n}(n=1,2,3，…)的前n项和S n满足S n＋a1=2a n，且a1，a2＋1，a3成等差数列，则a1＋a5=________.三、解答题13.在等差数列{a n}中，a4=10，且a3，a6，a10成等比数列，求数列{a n}前20项的和S20.14.已知数列{a n}的前n项和S n=2n-n2，a n=log5b n，其中b n>0，求数列{b n}的前n项和T n.15.已知数列{a n }的前n 项和S n =1＋λa n ，其中λ≠0.(1)证明{a n }是等比数列，并求其通项公式；(2)若S 5=，求λ.313216.设{a n }是公比大于1的等比数列，S n 为数列{a n }的前n 项和．已知S 3=7，且a 1＋3,3a 2，a 3＋4构成等差数列．(1)求数列{a n }的通项；(2)令b n =ln a 3n ＋1，n=1,2，…，求数列{b n }的前n 项和T n .答案解析1.答案为：D ；解析：a 1=2，q=2，∴S n ==2n ＋1-2.2× 1－2n1－22.答案为：B ；解析：设等比数列{a n }的公比为q ，由a 1=1，a 4=，得q 3=，解得q=，181812于是S 10===2-.a1 1－q10 1－q 1－ 12 101－121293.答案为：C ；解析：S 4==1，①S 8==17，②；②÷①得1＋q 4=17，a1· 1－q41－qa1· 1－q81－qq 4=16.q=±2.4.答案为：C ；解析：设数列{a n }的公比为q ，∵a 2·a 3=a ·q 3=a 1·a 4=2a 1，∴a 4=2.21又∵a 4＋2a 7=a 4＋2a 4q 3=2＋4q 3=2×，∴q=.∴a 1==16.S 5==31.5412a4q3a1· 1－q51－q5.答案为：C ；解析：a 3=3S 2＋2，a 4=3S 3＋2，等式两边分别相减得a 4-a 3=3a 3，即a 4=4a 3，∴q=4.6.答案为：D ；解析：根据前n 项和S n =2n -1，可求出a n =2n-1，由等比数列的性质可得{a }仍为等比数2n 列，且首项为a ，公比为q 2，∴a ＋a ＋…＋a =1＋22＋24＋…＋22n-2=(4n -1)．212122n 137.答案为：B ；解析：设S 2=k ，则S 4=3k ，由数列{a n }为等比数列(易知数列{a n }的公比q≠-1)，得S 2，S 4-S 2，S 6-S 4为等比数列，又S 2=k ，S 4-S 2=2k ，∴S 6-S 4=4k ，∴S 6=7k ，∴==，S6S47k 3k 73故选B.8.答案为：2n -1；解析：由=2，∴{a n }是以a 1=1，q=2的等比数列，故S n ==2n -1.an ＋1an 1× 1－2n1－29.答案为：；13解析：∵S 1,2S 2,3S 3成等差数列，∴4S 2=S 1＋3S 3，即4(a 1＋a 1q)=a 1＋3(a 1＋a 1q ＋a 1q 2)，∴4(1＋q)=1＋3(1＋q ＋q 2)，解之得q=.1310.答案为：-2；解析：设等比数列为{a n }，则a 1=S 1=3m ＋2，S 2=a 1＋a 2=9m ＋2⇒a 2=6m ，S 3=a 1＋a 2＋a 3=27m ＋2⇒a 3=18m ，又a =a 1·a 3⇒(6m) 2=(3m ＋2)·18m ⇒m=-2或m=0(舍去)．∴m=-2.211.答案为：2n -1；解析：由题意，Error!，解得a 1=1，a 4=8或者a 1=8，a 4=1，而数列{a n }是递增的等比数列，所以a 1=1，a 4=8，即q 3==8，所以q=2，a4a1因而数列{a n }的前n 项和S n ===2n -1.a1 1－qn 1－q 1－2n1－212.答案为：34；解析：由S n ＋a 1=2a n ，得a n =S n -S n-1=2a n -2a n-1(n≥2)，即a n =2a n-1(n≥2)．从而a 2=2a 1，a 3=2a 2=4a 1.又因为a 1，a 2＋1，a 3成等差数列，所以a 1＋a 3=2(a 2＋1)，所以a 1＋4a 1=2(2a 1＋1)，解得a 1=2，所以数列{a n }是首项为2，公比为2的等比数列，故a n =2n ，所以a 1＋a 5=2＋25=34.13.解：设数列{a n }的公差为d ，则a 3=a 4-d=10-d ，a 6=a 4＋2d=10＋2d ，a 10=a 4＋6d=10＋6d ，由a 3，a 6，a 10成等比数列，得a 3a 10=a ，26即(10-d)(10＋6d)=(10＋2d)2.整理，得10d 2-10d=0.解得d=0或d=1.当d=0时，S 20=20a 4=200；当d=1时，a 1=a 4-3d=10-3×1=7，于是S 20=20a 1＋d=20×7＋190=330.20×19214.解：当n≥2时，a n =S n -S n-1=(2n-n 2)-[2(n-1)-(n-1)2]=-2n ＋3，当n=1时，a 1=S 1=2×1-12=1也适合上式，∴{a n }的通项公式a n =-2n ＋3(n ∈N *)．又a n =log 5b n ，∴log 5b n =-2n ＋3，于是b n =5-2n ＋3，b n ＋1=5-2n ＋1，∴==5-2=.bn ＋1bn 5－2n ＋15－2n ＋3125因此{b n }是公比为的等比数列，且b 1=5-2＋3=5，125于是{b n }的前n 项和T n ==.5[1－(125)n ]1－12512524[1－(125)n ]15.解：(1)证明：由题意得a 1=S 1=1＋λa 1，故λ≠1，a 1=，a 1≠0.11－λ由S n =1＋λa n ，S n ＋1=1＋λa n ＋1得a n ＋1=λa n ＋1-λa n ，即a n ＋1(λ-1)=λa n .由a 1≠0，λ≠0得a n ≠0，所以=.an ＋1an λλ－1因此{a n }是首项为，公比为的等比数列，于是a n =n-1.11－λλλ－111－λ(λλ－1)(2)由(1)得S n =1-n .(λλ－1)由S 5=得1-5=，即5=.3132(λλ－1)3132(λλ－1)132解得λ=-1.16.解：(1)由已知得Error!解得a 2=2.设数列{a n }的公比为q ，由a 2=2，可得a 1=，a 3=2q ，2q又S 3=7，可知＋2＋2q=7，即2q 2-5q ＋2=0.解得q 1=2，q 2=.2q 12由题意得q>1，∴q=2，∴a 1=1.故数列{a n }的通项为a n =2n-1.(2)由于b n =ln a 3n ＋1，n=1,2，…，由(1)得a 3n ＋1=23n ，∴b n =ln 23n =3nln 2.又b n ＋1-b n =3ln 2，∴{b n }是等差数列，∴T n =b 1＋b 2＋…＋b n ==·ln 2.n b1＋bn 23n n ＋12故T n =ln 2.3n n ＋1 2。
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Book 5 Unit5 first aid高频词汇短语1．________n．& vt.帮助；援助；资助2．________adj.暂时的；临时的3．________vi.& vt.流血4．________n．毒药；毒害vt.毒害；使中毒5．________vt.&vi.倒；灌；注；涌6．________n．损伤；伤害→________v．使受伤，弄伤7．_____n．变化；多样(化)；多变(性)→________adj.各种各样的8．________adj.牢的；紧的；紧密的→________adv.紧地；牢牢地9．________adj.(动作)稳定有力的；坚定的→________adv.坚固地；稳定地10．________vt.&vi.治疗；对待；款待n．款待；招待→________n．治疗；疗法；对待；待遇11．________vt.涂；敷；搽；应用；运用vi.申请；请求；使用；有效→________n．申请人→________n．申请(书)12．______n．压力；挤压；压迫(感)→____v．挤压；压迫13. (对伤患者的)急救______________14. 生病______________15. 触电；电休克______________16. 榨出；挤出______________17. 反复；多次______________18. 在适当的位置；适当______________19. 若干；许多______________20. 找到______________21. 区别对待；有影响；起(重要)作用________22. 阻止……______________23. 烧伤______________单元重点单词句型1．aid n．& vt.帮助；援助；资助运用完成句子(1)她应该能够不用词典就能读懂这个。
She should be able to read this ________________ a dictionary.(2)我们上急救课时，相互做实践的对象。
In our_____________ , we practised on one another.(3)他们被控帮助他逃跑。
They were accused of ______________________________We were________in our investigation(调查)by the cooperation of the local police.A. stoppedB. treatedC. aimedD. aidedI have a Longman Dictionary of Contemporary English，which is an important ________ learning English.A. aid inB. aid toC. help toD. help at2．apply vt.涂；敷；搽；应用；运用vi.申请；请求；使用；有效运用--完成句子(1)从这所著名的大学毕业后，我将把我学到的知识应用到日常工作中。
When I graduate from this famous university, I'll _____ what I have learnt everyday work.(2)学生们应该专心学习。
Students should ________________________________study.(3)——我失业好长时间了。
——真的吗？为什么不在我的公司申请一份工作呢？—I'm out of work for a long time.—Really? Why not ________ a job at my company?Only when you________what you have learned to practice________say you have made it.A. adapt; you canB. apply; can youC. use; you canD. adopt; can youOnce the new rules are made, what matters much next is how they will be________ to all the members of the club.A. devotedB. referredC. appliedD. directed3．fall ill (＝get ill/become ill/be ill) 生病运用---完成句子(1)因为这个坏消息他病倒了。
He ______ because of the bad news.(2)他由于自己不小心而受了伤。
He _________ because of his own carelessness.(3)他生气时就会大叫，这是常有的情形。
He shouts when he________, as is often the case.Because of the bad weather, my mother ________and lay in bed, she ________ for a week.A. has been ill; was illB. fell ill; has fallen illC. fell ill; has been illD. fell ill; is illOn landing from the sea yesterday, he________，so he may be absent from the meeting.A. fell illB. was illC. fall illD. is ill4．squeeze out 榨出；挤出运用:完成句子(1)那个柠檬看来已经干了，但也许你还能挤出几滴来。
The lemon looks dry, but you may be able to _____ a few drops.(2)每年他们都榨取很多的菠萝汁。
Every year they_ _ much juice _ __ the pineapples.5．in place 在适当的位置；适当运用:完成句子(1)她的衣服不适合在会议上穿。
Her dress is _______ at the meeting.(2)所有东西用过以后要放回原处。
Everything should be put ______ after use.Maggie is a neat and tidy student, who likes to have everything________.A. in publicB. in placeC. in returnD. in practiceWith everything needed________，she declared that the party began.A. in the place B taking placeC. out of placeD. in place6．make a difference 区别对待；有影响；起(重要)作用运用:完成句子(1)这次旅行对他以后的人生有影响。
The travel________ to his later life.(2)让警察知道一些证据关系重大。
It _______ to inform the policemen of some evidence.I read the poem__________.You have to be very exact in this job, because a small mistake can make a big________.A. similarityB. explanationC. instructionD. differenceShe thought it was worthwhile for her to teach in the small village to make a________ to the life of the children there.A. differenceB. senseC. studyD. discovery7、vital 至关重要的，生死攸关的完成句子①If the injuries are second or third degree burns, the doctor or hospital at once.如果是二度或者三度烧伤，至关重要的是把伤者立刻送去看医生或送往医院。
②Consideration for other people all of us.对我们所有人而言体谅别人是极其重要的。
③As far as I'm concerned, regular exercise our health.就我个人而言，经常锻炼对我们的健康非常重要。
[2012·安徽卷]Interest is as ________ to learning as the ability to understand, even more so.A. vitalB. availableC. specificD. similar8、treat v. 治疗，对待，款待n.款待，招待(一)归纳同类，拓展联想完成句子①John used these to the most severe injuries Ms Slade's hands.约翰就用这些东西把斯莱德女士手上最重的伤口包扎起来。
②Rules help us live together in harmony, because they show us the right way to others规则帮助我们和谐得在一起生活，因为规则向我们展示了对待他人正确的方式。
③His parents are dead and he lives with a family that .他的父母死了，他与一个对他不好的家庭住在一起。
④Let's go out for dinner－this time.咱们出去吃饭吧！这次我请客。
I still remember many years ago he________us to a good dinner on New Year's Day.A. aidedB. pouredC. appliedD. treated－This afternoon let's go to a good restaurant.－Oh, it'll cost a lot of money.－Don't worry. It is my________ today.A. serviceB. offerC. turnD. treat重点句型1、原句：So, as you can imagine, if your skin gets burned it can be very serious.因此，就如你能想到的，如果你的皮肤受到伤害，那它会是很严重。