问题 填空题
在数列{an}中,an=4n-
5
2
a1+a2+…+an=an2+bn
,其中a,b为常数,则a+2b的值为______.
答案

由题意可得an+1-an=4(n+1)-

5
2
-4n+
5
2
=4,

故数列{an}为等差数列,可得a1=

3
2

∴a1+a2+…+an=

n(
3
2
+4n-
5
2
)
2
=2n2-
1
2
n,

由题意可知a1+a2+…+an=an2+bn,

∴a=2,b=-

1
2

∴a+2b=2+2(-

1
2
)=1,

故答案为:1

阅读理解

阅读短文,选择正确答案。

       Happiness is for everyone. You don't need to care about the rich. Though they have beautiful houses with

large gardens and swimming pools, they may often feel lonely (孤独的). In fact, happiness is always around you

if you put your heart into it. When you are in trouble at school, your teachers will help you; when you do

something wrong, people around you feel unhappy; when you succeed in something, your friends will say

congratulations (祝贺) to you. All these are your happiness. If you notice a bit of them, you can see that

happiness is always around you.

       Happiness is not the same as money. It is a feeling of your heart. Although you are poor, you can also say

you are very happy. Money is not everything. You have something else that money can't buy. When you meet

with difficulties, you can loudly say you are very happy because you have more chances to challenge (挑战)

yourself. So you can not always say you are poor and you have bad luck. If you take every chance you get, you

can be a happy and lucky person.

1. ______ may often feel lonely even though they have beautiful houses with large gardens. [ ]

A. Teachers

B. Parents

C. Old people

D. Rich people

2. What will your friends say to you when you make great progress (进步)?[ ]

A. Congratulations.

B. That's all right.

C. It's very nice of you.

D. Not at all.

3. When you have more chances to challenge yourself, you may feel _______. [ ]

A. proud

B. lonely

C. happy

D. excited

4. You can make yourself happy by ______. [ ]

A. making much money

B. taking every chance you have

C. owning beautiful big houses

D. having nice cars

5. We can learn from the passage that _______. [ ]

A. poor people are always unhappy because they don't have money to buy big houses

B. we can find happiness around us even if we don't have much money

C. no one will help you if you are poor

D. rich people are very proud because they have big houses and nice cars

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