SOLUTION: A sequence has constant second differences of 2. The first of the first differences is 1. Complete the sequence, with the 1st term at 27. ------,-------,------,------,------

Suppose the second term is x and the third term y

sequence to 3 terms:    27      x        y
First differences          x-27    y-x  
Second difference               2

That means x-27=1
              x=28

That means (y-x)-(x-27) = 2 
               y-x-x+27 = 2
                y-2x+27 = 2
                   y-2x = -25 

Substitute x=28
                      y = 2(28)-25
                      y = 56-25
                      y = 31

So the difference table above becomes:

sequence to 3 terms:    27     28      31
First differences           1      3  
Second difference               2 

To extend the table to 2 more terms put 2 more 2's on the line with
the secnd differences, and put letters A and B for the next two terms
and C and D for the next two first differences. 

sequence to 5 terms:    27     28      31       A       B
First differences           1      3        C       D   
Second difference               2       2       2

Now we work backwards:
C must be 5 so that C-3 will equal 2

sequence to 5 terms:    27     28      31       A       B
First differences           1      3        5       D   
Second difference               2       2       2
 
D must be 7 so that D-5 will equal 2

sequence to 5 terms:    27     28      31       A       B
First differences           1      3        5       7   
Second difference               2       2       2

A must be 36 so that A-31 will equal 5

sequence to 5 terms:    27     28      31      36       B
First differences           1      3        5       7   
Second difference               2       2       2

Finally B must be 43 so that B-36 will equal 7

sequence to 5 terms:    27     28      31      36       43
First differences           1      3        5       7   
Second difference               2       2       2

So the next two terms are 36 and 43

Edwin