Consecutive Integer Word Problems
Consecutive integer problems are word problems that involve consecutive integers. Consecutive integers are integers that follow in sequence, each number being 1 more than the previous number, represented by n, n +1, n + 2, n + 3, ..., where n is any integer. For example: 23, 24, 25, … If we start with an even number and each number in the sequence is 2 more than the previous number then we will get consecutive even integers. For example: 16,18, 20, … If we start with an odd number and each number in the sequence is 2 more than the previous number then we will get consecutive odd integers. For example: 33, 35, 37, …
We will look at some examples of consecutive integer problems, consecutive odd integer problems and consecutive even integer problems.
Example : Consecutive Integer Problem The sum of the least and greatest of 3 consecutive integers is 60. What are the values of the 3 integers? Solution: Step 1: Assign variables :
Translate sentence into an equation. Sentence: The sum of the least and greatest is 60. Rewrite sentence:
Step 2: Solve the equation Combine like terms
Isolate variable x
Step 3: Check your answer
The question wants all the 3 consecutive numbers: 29, 30 and 31 Answer: The 3 consecutive numbers are 29, 30 and 31.
The following video shows an example of a consecutive number word problem:
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