 # Consecutive Integer Problems. What is a consecutive integer? Integer: natural numbers and zero Integer: natural numbers and zero Consecutive: one after.

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Consecutive Integer Problems

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

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

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

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

Answer The consecutive numbers are 8, 9, 10

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

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

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

Consecutive Even/Odd Integer Problems What if you wanted to find consecutive even or consecutive odd numbers? What if you wanted to find consecutive even or consecutive odd numbers?ODD 1 351 351 351 35 nn+2n+4 EVEN 2 462 462 462 46 +2+4 +2+4

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

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

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.

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