SOLUTION: the first difference of a sequence is 2, 3, 4, 5,... The sum of the first two terms of the original sequence is 16. What first three terms of original sequence?

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