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, …What are consecutive even integers?
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, …What are consecutive odd integers?
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 now look at some examples of consecutive even integer problems.
The following diagram shows an example of consecutive even integer problem. Scroll down the page for more examples and solutions on how to solve consecutive even integer problems.
Example : Consecutive Even Integer
John has a board that is 3 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.
Let x = length of first shelf
x + 2 = length of second shelf
x + 4 = length of third shelf
x + 6 = length of fourth shelf
Step 2: Convert 3 feet to inches
3 × 12 = 36
Step 3: Sum of the 4 shelves is 36
x + x + 2 + x + 4 + x + 6 = 36
Combine like terms
4x + 12 = 36
Isolate variable x
4x = 36 – 12
4x = 24
x = 6
Step 3: Check your answer
6 + 6 + 2 + 6 + 4 + 6 + 6 = 36
The lengths of the shelves should be 6, 8, 10 and 12.
Answer: The lengths of the shelves in inches should be 6, 8, 10 and 12.
How to represent the sum of even and odd consecutive integers algebraically?
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