Consecutive Integer Problems

1. Consecutive Integer Problems

2. What is a consecutive integer? • Integer: natural numbers and zero • Consecutive: one after the other Ex. 1, 2, 3 or 17, 18, 19

3. Setting Up a Consecutive Integer Word Problem There are 3 consecutive integers whose sum is 27. Find the integers.

4. Variables If n = the first consecutive integer then what is the second consecutive integer? Example) 1 2 3 n n+1 n+2 n = first consecutive integer n+1 = second consecutive integer n+2 = third consecutive integer +1 +2

5. Equation There are 3 consecutive integers whose sum is 27. Find the integers. n + (n+1) + (n+2) = 27 1st 2nd 3rd

6. Answer The consecutive numbers are 8, 9, 10

7. Your Turn There are 3 consecutive integers whose sum is 333. Find the integers.

8. Solution n = first consecutive integer n+1 = second consecutive integer n+2 = third consecutive integer first+ second + third = 333

9. Solution Continued n = 110 n+1 = 111 n+2 = 112 Check 110 + 111 + 112 = 333 221 + 112 = 333 333 = 333 The three consecutive integers are 110, 111, and 112

10. +2 +4 +2 +4 Consecutive Even/Odd Integer Problems • What if you wanted to find consecutive even or consecutive odd numbers? ODD 1 3 5 n n+2 n+4 EVEN 2 4 6 n n+2 n+4

11. Practice There are 2 consecutive odd integers whose sum is 36. Find the integers.

12. Another Try There are three consecutive even integers whose sum is 54. Find the integers. n = the first even integer n+2 = the second even integer n+4 = the third even integer

13. Solution n + (n+2) + (n+4) = 54 3n + 6 = 54 3n = 48 n = 16 n+2 = 18 n+4 = 20 Check 16 + 18 + 20 = 56 56 = 56 The 3 consecutive even integers are 16, 18 and 20.