问题 选择题
已知数列{an}满足3an+1+an=4(n∈N*)且a1=9,其前n项和为Sn,则满足不等式|Sn-n-6|<
1
125
的最小整数n是(  )
A.5B.6C.7D.8
答案

对3an+1+an=4 变形得:3(an+1-1)=-(an-1)

即:

an+1-1
an-1
=-
1
3

故可以分析得到数列bn=an-1为首项为8公比为-

1
3
的等比数列.

所以bn=an-1=8×(-

1
3
)n-1

an=8×(-

1
3
)n-1+1=bn+1

所以Sn=Sbn+n=

8[1-(-
1
3
)
n
]
1-(-
1
3
)
+n=6-6×(-
1
3
)
n
+n

|Sn-n-6|=|-6×(-

1
3
)n|<
1
125

解得最小的正整数n=7

故答案为C.

阅读理解

阅读短文并回答问题。

     The U.S. is one of the English-speaking countries in the world. In the U. S., people speak English. People

in the UK, Australia, Canada and New Zealand also speak English. But American English is different from the

English in the UK, or in Australia, for example, to say "去看电影", people in the U. S. say "to go to the movie

theater", while people in the UK say,"to go to the cinema." To say "裤子", people in the U.S. use pants.While

people in the UK say "trousers." American people say "sure" while people in the UK say "of course".

1. What are the English-speaking countries?

                                                                                                                                   

2. What language do the people in New Zealand speak? 

                                                                                                                                   

3. To say "去看电影", what do the people in the UK, say?

                                                                                                                                   

4. To say "裤子", what do the people in the US say?

                                                                                                                                   

5. When an American boy meets a boy from the UK, do they understand each other?

                                                                                                                                   

单项选择题