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An introduction to consecutive integers appeared in Consecutive Integer Expressions.
This lesson will utilize consecutive integer expressions in equations.
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Consecutive integers are numbers that continuously follow each other, in a counting order or pattern. The difference between two adjacent numbers is always the same value. The order is generally from smallest to largest. |
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Consecutive Integers: 1, 2, 3, 4, ... or x, x + 1, x + 2, x + 3, ...
Consecutive Even Integers: 2, 4, 6, 8, ... or x, x + 2, x + 4, x + 6 ...
Consecutive Odd Integers: 1, 3, 5, 7, ... or x, x + 2, x + 4, x + 6 ...
 For this course, whether the starting value, x,
is odd or even is determined by the statement of the problem.
1. Find three consecutive integers whose sum is 48.
Solution: Represent the three consecutive integers as x, x + 1 and x +
2.
x + (x + 1) + (x + 2) = 48
3x + 3 = 48
3x = 45
x = 15 So x + 1 = 16 and x + 2 = 17
ANS: 15, 16, 17
2. The product of two consecutive numbers is 132. Find the two consecutive integers.
Solution: Represent the two consecutive integers as x and x + 1.
x • (x + 1) = 132
x2 + x = 132
x2 + x -132 = 0
(x + 12)(x - 11) = 0
x = -12 x = 11
ANSWERS: x = 11 and x + 1 = 12 OR x = -12 and x + 1 = -11
Remember that consecutive integers can also be negative numbers.
3. The sum of two consecutive even integers is 46. Find these two even integers.
Solution: Represent the two consecutive even integers as x and x + 2.
x + (x + 2) = 46
2x + 2 = 46
2x = 44
x = 22
ANS: x = 22 and x + 2 = 24.
4. The sum of three consecutive odd integers is 39. Find the product of these three integers.
Solution: Represent the three consecutive odd integers as x, x + 2 and x +
4.
x + (x + 2) + (x + 4) = 39
3x + 6 = 39
3x = 33
x = 11, x + 2 = 13, x+
4 = 15
ANS: (product) 11 • 13 • 15 = 2145.
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