Starting to Explore Four Consecutive Numbers

Take four consecutive numbers, $a$, $b$, $c$, $d$.
 

1. (a) The four consecutive numbers sum to $130$. What are they?
   (b) The four consecutive numbers sum to $-38$. What are they?
    
2. The sum of the first three consecutive numbers is $10$ more than the fourth. What are the four numbers?
    
3. What is $(a+d)-(b+c)$? Why?
    
4. Explore $a+b+c-d$.

If you enjoyed working on this problem, you may now want to take a look at the follow-up problem, Continuing to Explore Four Consecutive Numbers.