Consecutive Even Integer 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 Even Integer

John has a board that is 6 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?

Solution:

Step 1: Being consecutive even numbers we need to add 2 to the previous number.

Assign variables :

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 6 feet to inches

6 × 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.

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