Consecutive Odd 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.

The following are common examples of consecutive integer problems.

Example : Consecutive Odd Integer

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?

Solution:

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

Assign variables :

Let x = length of shortest side

x + 2 = length of medium side

x + 4 = length of longest side

Sketch the figure

Step 2: Write out the formula for perimeter of triangle.

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

45 = x + x + 2 + x + 4

Combine like terms

45 = 3x + 6

Isolate variable x

3x = 45 – 6

3x = 39

x =13

Step 3: Check your answer

13 + 13 + 2 + 13 + 4 = 45

Be careful! The question requires the length of the longest side.

The length of longest = 13 + 4 =17

Answer: The length of longest side is 17

The following video shows how the solve the integer word problem:
The sum of three consecutive odd integer is 69. Find the integers.

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