3, 14, 27, ?, 63, 86, 115
  
Form the first and second differences.
Subtract each number from the one to the right of
it and write it underneath the number.  For instance
the 11 came from subtracting 14-3 getting 11 and 
writing 11 underneath 3.  And when there is no number
to subtract write a question mark there:

  3, 14, 27, ?, 63, 86, 115
 11, 13, 16, ?, 23, 29
  2,  3,  ?, ?,  6

The bottom line seems to go 2, 3, 4, 3, 6, 3, 8, 3, 10, 3, 12, 3, ...

So we can put 4 and 3 where the bottom two question marks are, 
then work backwards and get 20 between the 16 and the 23 on the
middle row, and that makes the missing number on the top row 43.

  3, 14, 27, 43, 63, 86, 115
 11, 13, 16, 20, 23, 29
  2,  3,  4,  3,  6

Answer: 43

Edwin