There are two methods.  

First method.  Differences:

list them with an x where the ? is
 

  9 
 19 
 40 
  x 
146
 
Beside each of the the first four numbers write the difference between
the next number below it.  That is,

Beside the 9 write 19-9 = 10
Beside the 19 write 40-19 = 21
Beside the 40 write x-40
Beside the x write 146-x which is 146-x
The numbers in the second column below are called "the first differences".

 
  9      10
 19      21
 40    x-40
  x   146-x 
146
 

Do the same as before:
Beside the 10 write 21-10 = 11
Beside the 21 write (x-40)-21 = x-40-21 = x-61
Beside the x-40 write (146-x)-(x-40) = 146-x-x+40 = 186-2x
The numbers in the third column below are called "the second differences".
 
  9      10       11
 19      21     x-61
 40    x-40   186-2x 
  x   146-x 
146
 
Beside the 11 write (x-61)-11 = x-61-11 = x-72
Beside the x-61 write (186-2x)-(x-61) = 186-2x-x+61 = 247-3x
The numbers in the fourth column below are called "the third differences".



  9      10       11      x-72
 19      21     x-61    247-3x
 40    x-40   186-2x 
  x   146-x 
146
 
Beside the x-72 write (247-3x)-(x-72) = 247-3x-x+72 = 319-4x
There is only one fourth differences.  We set it equal to 0.
 

  9      10       11      x-72   319-4x
 19      21     x-61    247-3x
 40    x-40   186-2x 
  x   146-x 
146
 
Set 319-4x = 0
       -4x = -319
         x = 319/4 
           
That's the missing value.

-----------------------------

Second method, find the polynomial equation for 

  9 = a1  
 19 = a2 
 40 = a3 
  x = a4 
146 = a5

Assume 

Substitute  and 




Substitute  and 




Substitute  and 




Substitute  and 




So we have the system of equations:



Solve that and get , , , 

So 



becomes:





So the missing term a4 is found by substituting n=4















Edwin