Starting to explore four consecutive numbers

Problem



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.



With thanks to Don Steward, whose ideas formed the basis of this problem.