问题 填空题
a1,a2,a3,a4是各项不为零的等差数列且公差d≠0,若将此数列删去某一项得到的数列(按原来的顺序)是等比数列,则
a1
d
的值为______.
答案

a2=a1+d  a3=a1+2d  a4=a1+3d

若a1、a2、a3成等比数列,则a22=a1•a3

(a1+d)2=a1(a1+2d)

a12+2a1d+d2=a12+2a1d

d2=0

d=0 与条件d≠0矛盾

若a1、a2、a4成等比数列,则a22=a1•a4

(a1+d)2=a1(a1+3d)

a12+2a1d+d2=a12+3a1d

d2=a1d

∵d≠0

∴d=a1

a1
d
=1

若a1、a3、a4成等比数列,则a32=a1•a4

(a1+2d)2=a1(a1+3d)

a12+4a1d+4d2=a12+3a1d

4d2=-a1d

∵d≠0

∴4d=-a1

a1
d
=-4

若a2、a3、a4成等比数列,则a32=a2•a4

(a1+2d)2=(a1+d)(a1+3d)

a12+4a1d+4d2=a12+4a1d+3d2

d2=0

d=0 与条件d≠0矛盾

综上所述:

a1
d
=1 或
a1
d
=-4

故答案为1或-4

选择题
完形填空
完型填空。
     While in the army there was nothing I dislike so much as the map-reading course,for the simple reason
that I always feel   1   even with a map in my hand. For weeks I had   2   awake at night thinking of the   3  
 test I would have to face at the end of the course.   4   the evil day arrived. It was my responsibility to lead
a small band of soldiers back to camp from the middle of   5  . We were driven out in a(n)   6   lorry and left
in a ploughed field with   7   to get back to camp as quickly as possible.
     Well knowing my   8  , the soldiers smiled as they saw me looking at the map and they made all sorts of
helpful suggestions. I folded the map up, put it in my pocket, and said that we would   9   east. After walking
through the cornfield for over an hour we came to a wide stream. I looked at the map  10 . It seemed to be 
 11  with masses of thin blue lines. But Which  12  line was this steam? In despair, we sat down in the cool 
 13  and I feel 1ike  14  the map into the water. Fifteen minutes later, a boat passed and I asked the boatman
if he could give us a  15  to the nearest village. I  16  that we had been out for a walk and  17  got lost. The
boatman invited us on  18  and I felt  19  when he told me that he had helped hundreds of soldiers to pass their
map-reading test! Not long  20 , we got off that boat and, following the boatman's instructions, took a bus into
the village and get back to camp.
( )1.A. stupid    
( )2.A. suffered  
( )3.A. basic      
( )4.A. At last     
( )5.A. village    
( )6.A. closed    
( )7.A. suggestions 
( )8.A. weakness  
( )9.A. head      
( )10.A. gradually 
( )11.A. spread    
( )12.A. similar  
( )13.A. tent      
( )14.A. tearing  
( )15.A. lift      
( )16.A. declared  
( )17.A. altogether 
( )18.A. board    
( )19.A. afraid    
( )20.A. ago      
B. blind    
B. lain      
B. actual    
B. At once  
B. downtown  
B. advanced  
B. directions 
B. thought  
B. point    
B. therefore 
B. painted  
B. particular
B. shadow    
B. throwing
B. hand      
B. pretended     
B. almost    
B. boat      
B. foolish  
B. late      
C. puzzled    
C. slept      
C. practical  
C. As a result
C. nowhere    
C. ordinary  
C. information 
C. task      
C. march      
C. merely    
C. covered    
C. correct    
C. shore      
C. striking  
C. favor      
C. admitted  
C. possible  
C. purpose    
C. fortunate  
C. afterwards     
D. lost         
D. 1aid         
D. special      
D. After all    
D. forest       
D. damaged      
D. instructions              
D. strength     
D. guide        
D. again        
D. separated    
D. wonderful    
D. shade        
D. destroying   
D. service      
D. described    
D. somehow      
D. platform     
D. interested   
D. away