SOLUTION: Which option is correct? 5 , ? , 4 , 7.5 , 17 , 45 A. 3.5 B. 3 C. 2.5 D. 2

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Question 826893: Which option is correct?
5 , ? , 4 , 7.5 , 17 , 45
A. 3.5
B. 3
C. 2.5
D. 2
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
5, ?, 4, 7.5, 17, 45

Let x be the missing number

5, x, 4, 7.5, 17, 45

List all 6 terms in a column
  
 5                                                                           
 x                                                                         
 4                                             
 7.5                             
17                   
45

Subtract each number or expression from the one immediately
underneath it, write it out beside that number in a new column
and simplify, if necessary

 5    x-5                                                                     
 x    4-x                                                                
 4    7.5-4=3.5                                  
 7.5  17-7.5=9.5               
17    45-17=28
45

Make a third column the same way

 5    x-5        (4-x)-(x-5)=9-2x                                             
 x    4-x        3.5-(4-x)=x-.5                                          
 4    7.5-4=3.5  9.5-3.5=6                    
 7.5  17-7.5=9.5 28-9.5=18.5
17    45-17=28
45

Make more columns the same way.  Continue until there are just two
in the last column

 5    x-5        (4-x)-(x-5)=9-2x (x-.5)-(9-2x)=3x-9.5 (6.5-x)-(3x-9.5)=16-4x
 x    4-x        3.5-(4-x)=x-.5   6-(x-.5)=6.5-x       12.5-(6.5-x)=6+x
 4    7.5-4=3.5  9.5-3.5=6        18.5-6=12.5
 7.5  17-7.5=9.5 28-9.5=18.5
17    45-17=28
45

Set the two expressions in the last column equal to each other:

16-4x = 6+x
   10 = 5x
    2 = x 

The missing number is 2.

Edwin
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