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Consecutive Integers
Consecutive integers are integers that follow one another in order with no gaps, each exactly one unit apart. Examples include:
Because each integer in the sequence is one more than the one before it, consecutive integers can be represented algebraically using a single variable. If the first integer is , then:
- = 1st integer
- = 2nd consecutive integer
- = 3rd consecutive integer
and so on. This pattern follows from the observation that the next consecutive integer after is one more than , which equals . Representing consecutive integers through a single variable is particularly useful in number problems, because it converts verbal descriptions like "three consecutive integers whose sum is " into a single-variable equation that can be solved with standard algebraic techniques.
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Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
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Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax
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