CONSECUTIVE INTEGERS



8E CONSECUTIVE INTEGERS

Consecutive Integers: 8, 9, 10 ( n, (n+1), (n+2) etc…

+1 +1

Consecutive Even Integers: 6, 8 ,10 ( n, (n+2), (n+4) etc…

+2 +2

Consecutive Odd Integers: 5, 7 ,9 ( n, (n+2), (n+4) etc..

+2 +22

a) Write equation using smaller, larger, largest etc..

b) Replace smaller, larger, largest etc… with n, (n+1), (n+2) or n, (n+2), (n+4) etc..

c) Solve the new equation.

Ex: Find two consecutive integers whose sum is -51

Smaller + larger = -51 n, (n+1)

n + (n+1) = -51

n + n + 1 = -51

2n + 1 = -51

2n = -52

n = -26 so -26 and -25

Ex: Find three consecutive odd integers such that the sum of the first and twice the largest is 101

Small + 2 largest = 101 n, (n+2), (n+4)

n + 2 (n+4) = 101

n + 2n + 8 = 101

3n + 8 = 101

3n = 93

n = 31 so 31, 33,35

1) Practice

2) Find two consecutive integers whose sum is 75.

3) Find four consecutive odd integers who sum is 128.

4) Find two consecutive even integers such that the sum of the larger and 3 times the smaller is 234.

5) Find three consecutive odd integers such that the sum of 7 times the smallest and twice the largest is –91.

6) There are four consecutive odd integers such that the sum of the first two is 8 less than the sum of the last two. What is the first integer?

7) There are three consecutive integers such that twice the largest plus the smallest is 64. Find the middle integer.

Consecutive Integers (Using Quadratics)

Ex: Find two consecutive even integers whose product Ex: Find middle of 3 consecutive odd integers such that the

is 528 n,(n+2) product of the smallest and the largest is 165. n, (n+2), (n+4)

Smaller(larger) = 528 Smallest(largest) = 165

n(n+2) = 528 n(n+4) = 165

n2 + 2n = 528 n2 + 4n = 165

n2 + 2n – 528 = 0 n2 + 4n – 165 = 0

n2 – 22n + 24n – 528 = 0 n2 – 11n + 15n – 165=0

n(n-22) + 24(n-22)=0 n(n-11) + 15(n-11) = 0

(n-22)(n+24) =0 (n-11)(n+15) = 0

n=22 n=-24 n=11 n=-15

22,24 and -24,-22 11,13,15 and -15,-13, -11 so answer is 13 and -13

7) Find two consecutive even integers whose product is 288.

8) Find two consecutive odd integers whose product is 195

9) Find three consecutive integers such that the sum of the largest number plus the product of the smaller two integers is 122.

10) Find the smallest of three consecutive integers such that the product of the largest two integers is 626 more than the smallest integer.

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