We have this information.  Put blanks for the unknown values:

n  an  1st diffs   
1  a1                   
           2
2  a2                  
           3
3  __                  
           4
4  __                   
           5
5  __
           6
6  __    

The sum of the first two terms of the original  sequence is 16

so a1 + a2 = 16
and the difference of a2 - a1 is 2

So we have the system:



So solve that system of equations and get 

 and 

So we fill those in:

n  an  1st diffs   
1   7                   
           2
2   9                  
           3
3  __                  
           4
4  __                   
           5
5  __
           6
6  __


Then we can fill in all the other blanks by adding the
next difference.









Edwin