How can I find the Answer to this? Addition problem.

[buffyc]

1 1 1 1

1 3 5 7

1 5 13 25

1 7 25 ?

[kempie]

79?  -  (3n+4)

[Marsh]

My guess is 55 for the reasons below.

You can always justify any number to replace the question mark by using the following procedure.  Subtract term 2 from term one and write it under the gap, term two from term three and write it under the gap, term three from,� etc. 
If you just get the same number add it to the last line and then to the last term. eg
1  1  1 ? gives 1   1   1   
                          0   0
To get the fourth term go 1 1 1 1
                                           0 0 0
1 3 5 ? gives 1 3 5 7  (and the series will continue 9    11  13 �)
                       2 2 2

[Marsh]

(Cont)1 3 5 ? gives 1 3 5 7  (9    11  13 �)
                      2 2 2
If  the second line has different numbers, do the same thing for the second line.
So 1   5   13  ? gives 1   5    13   25   (35   47   �)
        4  6                      4    6     8
          2                           2    2    

1   7   25   ? gives   1   7     25      55   (97�)
                                  6   18     30
                                     12   12

This procedure produces a series corresponding to the simplest equation of the form
y = a + bx + cx^2 + dx^3�. which fits the numbers given.   There is a routine for producing the equation from the triangle but I've forgotten what it is.

[Marsh]

(Cont)1 3 5 ? gives 1 3 5 7  (9    11  13 �)
                      2 2 2
If  the second line has different numbers, do the same thing for the second line.
So 1   5   13  ? gives 1   5    13   25   (35   47   �)
        4  6                      4    6     8
          2                           2    2    

1   7   25   ? gives   1   7     25      55   (97�)
                                  6   18     30
                                     12   12

This procedure produces a series corresponding to the simplest equation of the form
y = a + bx + cx^2 + dx^3�. which fits the numbers given.   There is a routine for producing the equation from the triangle but I've forgotten what it is.

[Marsh]

(Last bit and sorry for Part 2 twice)   The procedure produces a sensible number but it may not be the one the questioner intended.  (If you wanted the fourth term to be 56 then your triangle would go.

1   7     25      56        99
    6   18     31       45
       12   13     14
            1     1                                      )

But since it does give the right answers for all three of your examples, I'd think it works for the fourth.