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In these lessons, we will learn how to solve consecutive odd integer problems.

Related Topics:

Consecutive integer problems

Consecutive even integer problems.

Integer worksheets

Integer games

**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 are common examples of consecutive odd 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 :

Letx= 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 =Combine like termsx + x +2 +x+ 4

45 = 3Isolate variablex+ 6

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

Example: The sum of three consecutive odd integer is 231. What is the largest integer?.

(1) Find three consecutive even numbers whose sum is 84

(2) Find four consecutive odd numbers whose sum is 152

Example: Find three consecutive odd integers so that the sum of twice the first, the second and three times the third is 152.

Finding Integers That Are Consecutive, Consecutive Even, or Consecutive Odd.

This video goes through examples of finding consecutive integers, consecutive odd integers, & consecutive even integers that add up to a given number.

Example:

(1) The sum of three consecutive integers is 657; find the integers.

(2) The sum of three consecutive odd integers is 597; find the integers.

(3) The sum of three consecutive even integers is 528; find the integers.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.