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# Starting to Explore Four Consecutive Numbers

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

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Age 11 to 16

Challenge Level

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

- (a) The four consecutive numbers sum to $130$. What are they?

(b) The four consecutive numbers sum to $-38$. What are they?

- The sum of the first three consecutive numbers is $10$ more than the fourth. What are the four numbers?

- What is $(a+d)-(b+c)$? Why?

- 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.*