问题 解答题
在等比数列{an}中,an>0(n∈N*),公比q∈(0,1),a1a5+2a3a5+a2a8=25,且2是a3与a5的等比中项,
(1)求数列{an}的通项公式;
(2)设bn=log2an,数列{bn}的前n项和为Sn,当
S1
1
+
S2
2
+…+
Sn
n
最大时,求n的值.
答案

(1)∵a1a5+2a3a5+a2a8=25,且2是a3与a5的等比中项

∴a12q4+2a12q6+a12q8=25   ①

a12q6=4   ②

解①②的a1=16,q=

1
2

an=16•(

1
2
)n-1=(
1
2
)
n-5

故数列{an}的通项公式an=(

1
2
)n-5

(2)∵bn=log2an=5-n

Sn=

(9-n)n
2

Sn
n
=
9-n
2

当n=9时

Sn
n
=
9-n
2
=0

S1
1
+
S2
2
+…+
Sn
n
最大时,n=8或9

故n=8或9.

完形填空
完形填空。
     Many people around the world study English.  English is spoken in more
than forty _1   all over the world.  It is the only    2    that is spoken in so
many countries.  If you learn English well, it will be much easier for you
to   3   with people in English-speaking countries. It is not easy to learn
English,_4 you need to work hard. Where there is a will, there is a   5   . You can watch English   6    programs,English films on DVD or videos. You can   7   with your classmates in and out of class. You can speak to foreign
friends   8   the phone in English. You can also read English books,
newspapers and magazines and _ 9    letters or e-mails to your friends in
English.  If you study hard, you are    10    to make progress.
( )1. A. countries  
( )2. A. sport      
( )3. A. communicate
( )4. A.but        
( )5. A.road        
( )6. A.tape        
( )7. A.ask        
( )8. A.in          
( )9. A.write      
( )10.A.tired      
B. cities  
B. language
B. compete  
B.because  
B.street    
B.TV        
B.reply    
B.for      
B.send      
B.kind      
C. schools
C. culture
C. fight  
C.so      
C.path    
C.MP3      
C.talk    
C.to      
C.post    
C.sure    
D. villages    
D. art        
D. travel      
D.then        
D.way          
D.computer    
D.listen      
D.on          
D.give        
D.ready        
     
单项选择题