《大学数学A》第六章练习题

第一篇：《大学数学A》第六章练习题

《大学数学 A》

第二篇：大学数学第一层次练习题

大学数学第一层次第一学期期中练习题一

一、计算下列各题（简要写出计算过程）

sin(2x)2sinx1．求 lim.2．求

lim(xxx0arctan(2x)2arctanx

xtnxe11k

23.lim dt；4.lim3x3x0arctan(x2)ntnkk12xtln(1t),1dyd2y5．设 yxarctan，求 y,y.6．设 求 ,2.232xdxdxytt,3

3xxxx7．设 f(e)e,f(0)1,求f(x).8．cosxdx；9.earctanedx 

31sinxcosx2dx10.I1;

11.I.221sinx2

2x2x2.二、用N定义证明lim2xx

112xsin,

三、设f(x)xx(xsinx),四、已知f(lnx)x0,x0.求f(x)，讨论f(x)在x0的左、右连续性.xlnx,f(0)1,求f(1).2(1lnx)

五、设旋轮线xa(tsint),ya(1cost)(0t2,a0)与x轴围成一平面图形，求

1.该图形的面积；2.该图形边界的弧长；3.该图形绕y轴旋转一周的旋转体的体积.大学数学第一层次第一学期期中练习题二

一、计算下列各题（至少写一步演算过程）

1．求

.2．求

lim(xx.x0x03．计算limn

n

111.4.22222x0nn2n1n

25．f(2)3,lim

x

1f(53x)f(2)1

.6．设 yxarctan，求 y.x1x

xtln(1t),dy

yy(x)7．设由 确定，求.2

4dxy2tt,

8．设 yxe,y

2x

(10)

x2,求y(10)..9.已知y1x

.11.lnx

(1x)2.12.10．设 y2

cos2x,dydx

x

4



.xx2,0x1;

13.已知f(x)，设F(x)f(t)dt,(0x2).求F(x).1,1x2.二、1.用N语言证明lim

三、求极限 lim(sinx)

x

tan2x

2x

52.2．用语言证明lim(x23x)4.x1xx

1

.x2ln(1x2),x0,四、设f(x)

x0.2xsinx,1）求f(x)，讨论f(x)在x0的连续性；2）求 f(0).五、设0x14,xn1

n1,2,),，证明limxn存在，并求此极限.n

六、设f(x)在区间[0,)上可导，f(0)0,且其反函数为g(x)，若



f(x)0

g(t)dtx2ex，求f(x).七、求抛物线y2x与直线xy4所围图形的面积.大学数学第一层次第一学期期中练习题三

一、用极限定义证明下列极限：

x2

32（语言）(1)lim20（N语言）;(2)lim

x1x1nn2n

5二、求下列极限：

cosn5

cos(sinx)cosx1004

(1)limtan;(2)(3)lim(arctanx)lnx lim3x0x0nn4(ex1)(5x1)

n

arcsinx(4)limx0x

cot2x

（1x)x

1(5)limx；

x0(e1)ln(12x)

b2b(n1)b

sinasinasinasina

nnn(6).lim

nn

三、计算下列各题：(1)设yy(x)由

xarctant

2t

2ytye

5所确定，求

dy0()

.(2)设yx2lnx，求y1.dx

(3)

设yarctan(x(5)，求dy.(4).已知 f(x)x3sinx，求 f(10)(0).1xsinx2lnx

dx；(6)求x211x2dx；(7)求



ln0

.四、设x00,xn1

1(2xn2),n0,1,2,,求证数列xn收敛，并求其极限。3xn

五、已知曲线yax与曲线ylnx相切（即两曲线相交于一点，且在这一点有公共的切线）1.求a的值，2.求两曲线与x轴所围图形的面积.六、曲线ytannx在点(的切线交x轴于点(n,0)，求limy(n)4，1)

n

七、设f(x)是区间[-a,a](a>0)上的连续的偶函数.证明：

af(x)a1ex0f(x)dx a

第三篇：大学英语练习题

《大学英语

（三）》第2次作业

一、单选题（共 30 道试题，共 75 分。）得分：75 V

1.The football game will be played on ____C___.A.June sixB.six Junenm lkji

C.the sixth of JuneD.the six of June

2.Are you going to fix the car yourself, or are you going to have it ___D____? A.fixingB.to fixnm lkj

C.fixiD.fixed

3.—Can I help you carry the bag? —_______D_________.A.Needn’B.you couldn’t do

C.I could do it myself.D.Thank you, but I can manage it myself.4.They have learned about _______ in recent years.A.several hundreds English wordsi

B.hundreds of English wordsC.hundred of English wordsD.several hundred English word

5.—Do you think I could borrow your dictionary this weekend? —Sorry, but _____C___________ A.you can not have it right away.B.I'm sure you'll like IC.I'm going to need it myself.D.the dictionary is just there.6.She leaned ____B___ the wall while she was speaking to her friend.A.toB.againstC.towardsD.for

7.—Would you like something to drink? What about a cup of tea? —______A__________

A.No, thanks B.No, I wouldn'tC.Yes, I wantD.Yes, I like

8.The patients are quite _______ to the nurses for their special care.A.enjoyable B.helpful C.confidenti D.grateful

9.—Hello, may I have an appointment with the headmaster? —________________.A.Sorry, I don't know younm lkjB.No, you can'tiC.Certainly.Wait a minute, pleasenm lkjD.Let me see10.As long as the sun shines, the earth will not run out of energy.The sun pours more energy on earth than we can ever use.Most of that energy comes to us as heat and light.Energy from the sun is called solar energy.Anything to do with the sun is called “solar”.The word began with the Roman word for the sun and their god ofthe sun, who was called Sol.Solar energy is a safe kind of energy.It doesn't make pollution or have dangerous leftovers.That is why scientists and investors are experimenting with ways of harnessing（治理利用）the sun to do some of the jobs fossil fuels have been doing.But to make the sun do work like that, they have to solve some problems.They have to collect the sun's energy.Collecting sunshine is not easy, unless you are a plant.Sunshine is not easy to store, either.You can't fill a tank with it or put it in the wood box.You can not move it through a pipe or a wire.You can not just turnit on.(4)、What are the problems facing scientists who want to use solar energy? A.It is not easy to collect.B.It is not easy to store.nm lkjC.It is not easy to find out.iD.both A and B.11.Every morning Mr.Smith takes a _______ to his office.A.20 minutes' walkB.20 minute's walknm lkjC.20-minutes walkiD.20-minute walk12.As long as the sun shines, the earth will not run out of energy.The sun pours more energy on earth than we can ever use.Most of that energy comes to us as heat and light.Energy from the sun is called solar energy.Anything to do with the sun is called “solar”.The word began with the Roman word for the sun and their god ofthe sun, who was called Sol.Solar energy is a safe kind of energy.It doesn't make pollution or have dangerous leftovers.That is why scientists and investors are experimenting with ways of harnessing（治理利用）the sun to do some of the jobs fossil fuels have been doing.But to make the sun do work like that, they have to solve some problems.They have to collect the sun's energy.Collecting sunshine is not easy, unless you are a plant.Sunshine is not easy to store, either.You can't fill a tank with it or put it in the wood box.You can not move it through a pipe or a wire.You can not just turnit on.(1)、What form does most of solar energy take to reach us? A.Light.B.Heat.nm lkjC.gas.iD.both A and B.13.—Would you like to go skating with me? —________________.A.Yes, I think soB.No, thanksnm lkjiC.Yes, I'd love toD.I'm afraid not 14._______ the War of Independence, the United States was an English colony.iA.BeforeB.Atnm lkjC.InD.Between15.As long as the sun shines, the earth will not run out of energy.The sun pours more energy on earth than we can ever use.Most of that energy comes to us as heat and light.Energy from the sun is called solar energy.Anything to do with the sun is called “solar”.The word began with the Roman word for the sun and their god of the sun, who was called Sol.Solar energy is a safe kind of energy.It doesn't make pollution or have dangerous leftovers.That is why scientists and investors are experimenting with ways of harnessing（治理利用）the sun to do some of the jobs fossil fuels have been doing.But to make the sun do work like that, they have to solve some problems.They have to collect the sun's energy.Collecting sunshine is not easy, unless you are a plant.Sunshine is not easy to store, either.You can't fill a tank with it or put it in the wood box.You can not move it through a pipe or a wire.You can not just turnit on.(2)、Where

does the word “solar” come from? A.Greek.iB.Roman.nm lkjC.Old English.D.Chinese.16.As long as the sun shines, the earth will not run out of energy.The sun pours more energy on earth than we can ever use.Most of that energy comes to us as heat and light.Energy from the sun is called solar energy.Anything to do with the sun is called “solar”.The word began with the Roman word for the sun and their god ofthe sun, who was called Sol.Solar energy is a safe kind of energy.It doesn't make pollution or have dangerous leftovers.That is why scientists and investors are experimenting with ways of harnessing（治理利用）the sun to do some of the jobs fossil fuels have been doing.But to make the sun do work like that, they have to solve some problems.They have to collect the sun's energy.Collecting sunshine is not easy, unless you are a plant.Sunshine is not easy to store, either.You can't fill a tank with it or put it in the wood box.You can not move it through a pipe or a wire.You can not just turnit on.(3)、Which of the following is NOT true of solar energy? A.It is a safe energy.B.It is a green energy.nm lkjiC.It may cause pollution to the air.D.It is endless.17.—Could I see your ticket please? —________________A.I am not sure yetB.I'd love onenm lkjC.I might be.Why?iD.Here you are.18.—Why not join us in the game? —________________.iA.OK!I'm comingB.No, you do the samenm lkjC.Oh, that's all rightD.Don't mention it19.As long as the sun shines, the earth will not run out of energy.The sun pours more energy on earth than we can ever use.Most of that energy comes to us as heat and light.Energy from the sun is called solar energy.Anything to do with the sun is called “solar”.The word began with the Roman word for the sun and their god of the sun, who was called Sol.Solar energy is a safe kind of energy.It doesn't make pollution or have dangerous leftovers.That is why scientists and investors are experimenting with ways of harnessing（治理利用）the sun to do some of the jobs fossil fuels have been doing.But to make the sun do work like that, they have to solve some problems.They have to collect the sun's energy.Collecting sunshine is not easy, unless you are a plant.Sunshine is not easy to store, either.You can't fill a tank with it or put it in the wood box.You can not move it through a pipe or a wire.You can not just turn it on.(5)、What is the writer's purpose of writing the passage? iA.To give a brief introduction to solar energy.B.To explain the reason why it is not easy to make solar energy.nm lkjC.To give information about the advantages of solar energy.D.To give a brief introduction to the word “solar”.20.—Would you mind closing the window? It is windy outside.—________________ iA.Not at all.B.Sure, go ahead.nm lkjC.Why not?D.Yes, I would.21.Nancy is _______

girl.A.a eighteen-year-oldnm lkjB.an eighteen-years-oldC.a eighteen-years-oldnm lkjiD.an eighteen-year-old

22.When will you finish _______ the outing for next Friday?A.planB.to plannm lkjiC.planningD.planned23.It's _______ that he was wrong.A.clearlyB.claritynm lkjiC.clearD.clearing24.-It's a good idea.But who's going to _______ the plan?-I think John and Peter will.iA.carry outB.get throughC.take inD.set aside25.Eggs, though rich in nourishments, have _______ of fat.A.a large numberB.the large numbernm lkjiC.a large amountD.the large amount26.You'd better _______ in bed.It's bad for your eyes.A.not to readnm lkjiB.not readC.don't readjD.read27.The Japanese, _______ average, live much longer than the Europeans.A.withnm lkjB.inC.tonm lkjiD.on28.After the Minister of Education had finished speaking at the press conference, he was made _______ all sorts of awkward questions.A.answerB.answeringnm lkjC.answerediD.to answer29.—This box is too heavy for me to carry it upstaris.—________________.A.You may ask for help.iB.I’ll give you a hand.nm lkjC.Please do e a favor.D.I’d come to help.30.—Don't forget to come to my party this evening!—________________ A.I can't.iB.I won't.nm lkjC.I don't.D.I will.二、判断题（共 10 道试题，共 25 分。）得分：25 V《大学英语

（三）》第2次作业 试卷总分：100测试时间：--试卷得分：1001.A story is told about a soldier who was finally coming home after having fought in Vietnam.He called his parents from San Francisco.“Mom and Dad, I'm coming home, but I've a favor to ask.I have a friend.I'd like to bring him home with me.” “Sure,” they replied, “we'd love to meet him.”“There's something you should know,” the son continued, “he was injured pretty badly in the fighting.He stepped on a land mine（地雷）and lost an arm and a leg.He has nowhere else to go, and I want him to live with us.” “We're sorry to hear that, son.But, maybe we can help him find somewhere to live.” “No, Mom and Dad, I want him to live with us.”“Son,” said the father, “you don't know what you're asking.Someone with such a handicap would be a terrible burden to us.We have our own lives to live, and we can't let something like this interfere with our lives.I think you should just come home and forget about this guy.He'll find a way to live on his own.”At that point, the son hung up the phone.The parents heard nothing more from him.A few days later, however, they received a call from the San Francisco police.Their son had died after falling from a building.The

police believed he had killed himself.The grief-stricken（悲痛欲绝的）parents flew to San Francisco and were taken to the city morgue（太平间）to identify the body of their son.They recognized him, but to their horror they also discovered something they didn't know, their son had only one arm and one leg.(2)、The soldier told his parents that he wanted them to meet his friend in the army.iA.错误nmlkjB.正确2.The word “horsepower” was first used two hundred years ago.James Watt had made the world's first widely used steam engine.He had no way of telling people exactly how powerful it was, for at that time there were no units for measuring power.Watt decided to find out how much work one strong horse could do in one minute.He called that unit one horsepower.With this unit he could measure the work his steam engine could do.He discovered that a horse could lift a 3300-pound weight 10 feet into the air on one minute.His engine could lift a 33-pound weight 100 feet in one minute.Because his engine did ten times as much work as the horse, Watt called it a ten horsepower engine.(2)、Watt wanted to find a way to lift a 3300-pound weight.iA.错误nmlkjB.正确3.The word “horsepower” was first used two hundred years ago.James Watt had made the world's first widely used steam engine.He had no way of telling people exactly how powerful it was, for at that time there were no units for measuring power.Watt decided to find out how much work one strong horse could do in one minute.He called that unit one horsepower.With this unit he could measure the work his steam engine could do.He discovered that a horse could lift a 3300-pound weight 10 feet into the air on one minute.His engine could lift a 33-pound weight 100 feet in one minute.Because his engine did ten times as much work as the horse, Watt called it a ten horsepower engine.(4)、One horsepower would equal the weight of one horse.iA.错误nmlkjB.正确4.The word “horsepower” was first used two hundred years ago.James Watt had made the world's first widely used steam engine.He had no way of telling people exactly how powerful it was, for at that time there were no units for measuring power.Watt decided to find out how much work one strong horse could do in one minute.He called that unit one horsepower.With this unit he could measure the work his steam engine could do.He discovered that a horse could lift a 3300-pound weight 10 feet into the air on one minute.His engine could lift a 33-pound weight 100 feet in one minute.Because his engine did ten times as much work as the horse, Watt called it a ten horsepower engine.(3)、He made up a unit of measurement based on the strength of a horse.A.错误iB.正确 5.A story is told about a soldier who was finally coming home after having fought in Vietnam.He called his parents from San Francisco.“Mom and Dad, I'm coming home, but I've afavor to ask.I have a friend.I'd like to bring him home withme.” “Sure,” they replied, “we'd love to meet him.”“There's something you should know,” the son continued, “he was injured pretty badly in the fighting.He stepped on a land mine（地雷）and lost an arm and a leg.He has nowhere else to go, and I want him to live with us.” “We're sorry to hear that, son.But, maybe we can help him find somewhere to live.” “No, Mom and Dad, I want him to live with us.”“Son,” said the father, “you don't know what you're asking.Someone with such a handicap would be a terrible burden to us.We have our own lives to live, and we can't let something like this interfere with our lives.I think you should just come home and forget about this guy.He'll find a way to live on hisown.”At that point, the son hung up the phone.The parents heard nothing more from him.A few days later, however, theyreceived a call from the San Francisco police.Their son had died afterfalling from a building.The police believed he had killedhimself.The grief-stricken（悲痛欲绝的）parents flew to San Francisco and were taken to the city morgue（太平间）to identify the body of their son.They recognized him, but to their horror they also discovered something they didn't know, their son had only one arm and one leg.(5)、The son killed himself because he was unable to find a job.iA.错误nmlkjB.正确6.The word “horsepower” was first used two hundred years ago.James Watt had made theworld's first widely used steam engine.He had no way of telling peopleexactly how powerful it was, for at that time there were no units for measuring power.Watt decided to find out how much work one strong horse could do in one minute.He called that unit one horsepower.With this unit he could measure the work his steam engine could do.He discovered that a horse could lift a

3300-pound weight 10 feet into the air on one minute.His engine could lift a 33-pound weight 100 feet in one minute.Because his engine did ten times as much work as the horse, Watt called it a ten horsepower engine.(5)、The possible title for this passage is The Origin of the Term “Horsepower”.A.错误nmlkjiB.正确7.A story is told about a soldier who was finally coming home after having fought in Vietnam.He called his parents from San Francisco.“Mom and Dad, I'm coming home, but I've afavor to ask.I have a friend.I'd like to bring him home withme.” “Sure,” they replied, “we'd love to meet him.”“There's something you should know,” the son continued, “he was injured

pretty badly in the fighting.He stepped on a land mine（地雷）and lost an arm and a leg.He has nowhere else to go, and I want him to live with us.” “We're sorry to hear that, son.But, maybe we can help him find somewhere to live.” “No, Mom and Dad, I want him to live with us.”“Son,” said the father, “you don't know what you're asking.Someone with such a handicap would be a terrible burden to us.We have our own lives to live, and we can't let something like this interfere with our lives.I think you should just come home and forget about this guy.He'll find a way to live on hisown.”At that point, the son hung up the phone.The parents heard nothing more from him.A few days later, however, they received a call from the San Francisco police.Their son had died afterfalling from a building.The police believed he had killedhimself.The grief-stricken（悲痛欲绝的）parents flew to San Francisco and were takento the city morgue（太平间）to identify the body of their son.They recognized him, but to their horror they also discovered something they didn't know, their son had only one arm and one leg.(4)、A few days later the parents were told by the police that their son had killed himself.A.错误nmlkjiB.正确8.A story is told about a soldier who was finally coming home after having fought in Vietnam.He called his parents from San Francisco.“Mom and Dad, I'm coming home, but I've afavor to ask.I have a friend.I'd like to bring him home withme.” “Sure,” they replied, “we'd love to meet him.”“There's something you should know,” the son continued, “he was injured pretty badly in the fighting.He stepped on aland mine（地雷）and lost an arm and a leg.He has nowhere else to go, and I want him to live with us.” “We're sorry to hear that, son.But, maybe we can help him find somewhere to live.” “No, Mom and Dad, I want him to live with us.”“Son,” said the father, “you don't know what you're asking.Someone with such a handicap would be a terrible burden to us.We have our own lives to live, and we can't let something like this interfere with our lives.I think you should just come home andforget about this guy.He'll find a way to live on hisown.” At that point, the son hung up the phone.The parents heard nothing more from him.A few days later, however, they received a call from the San Francisco police.Their son had died after falling from a building.The police believed he had killed himself.The grief-stricken（悲痛欲绝的）parents flew to San Francisco and were taken to the city morgue（太平间）to identify the body of their son.They recognized him, but to their horror they also discovered something they didn't know, their son had only one arm and one leg.(3)、His father considered his plan unacceptable.A.错误nmlkjiB.正确9.A story is told about a soldier who was finally coming home after having fought in Vietnam.He called his parents from San Francisco.“Mom and Dad, I'm coming home, but I've a favor to ask.I have a friend.I'd like to bring him home with me.” “Sure,” they replied, “we'd love to meet him.”“There's something you should know,” the son continued, “he was injured pretty badly in the fighting.He stepped on a land mine（地雷）and lost an arm and a leg.He has nowhere else to go, and I want him to live with us.” “We're sorry to hear that, son.But, maybe we can help him find somewhere to live.” “No, Mom and Dad, I want him to live with us.”“Son,” said the father, “you don't know what you're asking.Someone with such a handicap would be a terrible burden to us.We have our own lives to live, and we can't let something like this interfere with our lives.I think you should just come home and forget about this guy.He'll find a way to live on his own.”At that point, the son hung up the phone.The parents heard nothing more from him.A few days later, however, they received a call from the San Francisco police.Their son had died after falling from a building.The police believed he had killed himself.The grief-stricken（悲痛欲绝的）parents flew to San Francisco and were taken to the city morgue（太平间）to identify the body of their son.They recognized him, but to their horror they also discovered something they didn't know, their son had only one arm and one leg.(1)、The soldier called his parents from San Francisco after having fought in Vietnam.A.错误nmlkjiB.正确10.The word “horsepower” was first used two hundred years ago.James Watt had made the world's first widely used steam engine.He had no way of telling people exactly how powerful it was, for at that time there were no units for measuring power.Watt decided to find out how much work one strong horse could do in one minute.He called that unit one horsepower.With this unit he could measure the work his steam engine could do.He discovered that a horse could lift a 3300-pound weight 10 feet into the air on one minute.His engine could lift a 33-pound weight 100 feet in one minute.Because his engine did ten times as much work as the horse, Watt called it a ten horsepower engine.(1)、The passage says that Watt made the first widely used steam engine.A.错误nmlkjiB.正确

第四篇：一年级数学练习题

小学一年级数学练习题

一、我是计算小能手：

1.口算。（15分）

67-7= 3+73= 4+56= 75-15= 56-7=

60+21= 70-20= 88-70= 96+4= 49+40=

81-8= 55-30= 16+8= 85-40= 50-7=

80-30= 26+9= 13+80= 45+54= 49-8=

70+2= 28-9= 6+64= 81-3= 20+57=

99-9= 53+4= 39+30= 78-20= 14+5=

2.竖式计算。（6分)

41+27= 57-34= 88－50=

二、动脑筋填一填。(29分）

1.在计数器上，从右边起，第一位是（）位，第（）位是百位。

2.56里有（）个十和（）个一。

3.30里面有（）个十。10个10 是（）。

4.十位是2，个位是９，这个数是（）；一个一个的数和它

相邻的数是（）和（）。

5.在○里填上“＜”、“＞”“＝”。（3分）

59-50○8 17+8○23 30+9○44-4

50+44○44+50 8+70○7+80 68-6○68-60

6.排一排。（3.5分）

44 97 80 67 31 29

（）＜（）＜（）＜()＜()＜()＜()

7.（1.5分）比57大比61小的数依次是（）、（）、（）。

8.（）-40=30（）-20 = 28

45-（）=15 39-（）=33

9.（4分）5元=（）角 3角 =（）分

6元7角 =（）角 2元 =（）角 =（）分

10.连一连。（4分）

大约6时 6时 9时 7时半

三、填一填。（10分）

四、按要求将你认为合适的答案圈起来。（5分）

1.书包的价钱比80元少一些。（90元、78元、82元）

2.玩具小汽车的价钱比60元贵多了！（68元、95元、48元）

3.和60最接近的数。（100、45、70、56）

4.54+3的和是（四十多、五十、五十多）

5.得数比50大的算式（59-9、59-10、59-8）

五、看图列式计算。（6分）

1.

=

36个 20个

2.

=

六、解决实际问题。（21分）

1.学校要把82箱文具送给山区小学，已送去50箱，还要送几箱？

2.树上小鸟飞走了25只，还剩下8只，树上原来有多少只？

3.学校田径队有38人，篮球队有20 人，乒乓球队有14人。

①田径队和篮球队一共有多少人？

②篮球队比乒乓球队多多少人？

4.9元 68元 30元 8元

（1）比 贵多少元？

（2）小红买了一个 找回2元，她付了多少钱？

（3）用50元可以买哪些商品？

七、考考聪明的你：〇里应该填几？（3分）

+ =32-= 15 + =（）

卷面5分

第五篇：数学等差数列练习题

练习题3：等差数列

1、已知等差数列的首项a1，项数n，公差d，求末项an

公式：末项=首项+（项数-1）×公差an= a1+（n-1）×d

（1）一个等差数列的首项为5，公差为2，那么它的第10项是（）。

2、已知等差数列的首项a1，末项an，公差d，求项数n

公式：项数=（末项-首项）÷公差+1n=（an－a1）÷d+1

（1）等差数列7、11、15……、87，问这个数列共有（）项。

（2）等差数列3、7、11…，这个等差数列的第（）项是43。

3、已知等差数列的首项a1，末项an，项数n, 求公差d

公式：公差=（末项-首项）÷（项数-1）d=（an－a1）÷（n－1）

（1）已知等差数列的第1项为12，第6项为27。求公差（）。

4、已知等差数列的末项an，项数n, 公差d，求首项a1

公式：首项=末项-（项数-1）×公差a1=an-（n-1）×d

（1）已知一个等差数列的公差为2，这个等差数列的第10项是为23，这个等差数列的首项是（）。

（2）一堆木料，最下层有24根，往上每一层都比下一层少2根，共10层，最上层有（）根木料。

5、把70拆成7个自然数，使这7个数从小到大排成一行后，相邻两个数的差都相等，那么，中间的数是（）。

6、5个连续奇数的和是35，其中最大的奇数是（）。

第二类：已知等差数列的首项a1，末项an，项数n,求和用公式：sn=（a1+ an）×n÷2［或 sn=中间数×项数］

1、已知等差数列2，5，8，11，14，17，20，求这个数列的和是（）。

2、等差数列7+11+15+19+23+27+31+35的和是（）。

3、求1+2+3+4+5+6+7+……+20=4、1+3+5+7+9+11+……+19=

5、已知等差数列的首项是5，末项是47，求这个数列共有8项求这个数列的和是（）。

6、王师傅每天工作8小时，第一小时加工零件5个，从第二小时起每小时比前一小时多加工相同的零件，第8小时加工了23个，王师傅一天加工零件（）个。

等差数列分组练习题

已知等差数列的首项a1，末项an，项数n,求和用公式：sn=（a1+ an）×n÷2

如果题中有缺项，需要先求缺项再求和

第一类缺项是（）

1、已知等差数列2，5，8，11，14…，求前11项的和是多少？

2、数列1、4、7、10、……，求它的前21项的和是多少？

第二类缺项是（）

1、等差数列7，11，15，……… 87，这个数列的和是多少？

2、已知等差数列5，8，11…47，求这个数列的和是多少？

第三类缺项是（）

1、一个剧场设置了16排座位，后每一排都比前一排多2个座位，最后一排有68个座位，这个剧场共有多少个座位？

2、有10个数，后一个比前一个多5，第10个数是100，求这10个数的和是多少？ 第四类缺项是（）

sn=中间数×项数1、5个连续奇数，第一个数和最后一个数的和是18，求这5个连续奇数的和是多少？