SOLUTION: what number question mark refers in the series 3,9,17,?,43

Let x be the missing number.
Make a table of differences by listing 
the terms in a column.  Then subtract
each number from the number just below
it.  Do this with each column until
there are just 2 in the last column:

       1st     2nd      3rd 
an    diff    diff     diff
---------------------------
 3       6       2     x+27 
 9       8    x-25    85-3x
17    x-17   2x-60
 x    43-x
43

Then set those two 3rd differences equal:

x+27 = 85-3x
  4x = 112
   x = 28

Answer: 28

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

To find the general term:

Assume



Then, substituting n=1,2,3,5 and the 
4 sequence values gives us this system
of equations:



Solve that system and get , , , 

  <---general term

Substituting  gives . 

Edwin