In these lessons, we will learn how to solve
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, …
The following diagram shows an example of a consecutive integer problem. Scroll down the page for more examples and solutions on consecutive integer problems.
Consecutive Integer Problems
Example 1: 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 equationCombine like terms
Isolate variable x
2x = 58
Step 3: Check your answer29 + 29 + 2 = 60
The question wants all the 3 consecutive numbers: 29, 30 and 31Answer: The 3 consecutive numbers are 29, 30 and 31.
The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?
Step 1: Being consecutive odd numbers we need to add 2 to the previous number.Assign variables:
Sketch the figure
Be careful! The question requires the length of the longest side.
The length of longest = 13 + 4 =17Answer: The length of longest side is 17
John has a board that is 5 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be in inches?
Step 1: Being consecutive even numbers we need to add 2 to the previous number.Assign variables:
The lengths of the shelves should be 12, 14, 16 and 18.Answer: The lengths of the shelves in inches should be 12, 14, 16 and 18.
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