Consecutive Odd Integer Problems

Consecutive Integers

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, …

The following are some examples of consecutive odd integer problems. Scroll down the page for more examples and solutions on consecutive odd integers.

 

How to solve consecutive integer word problems?

1. Represent the Integers Algebraically:
   Let ‘x’ be the first odd integer.
   The next consecutive odd integer is ‘x + 2’.
   The next after that is ‘x + 4’, and so on.
   If you need to represent a specific number of consecutive odd integers, continue adding 2 to the previous expression.
   
2. Translate the Word Problem into an Equation:
   Carefully read the problem and identify the relationship between the consecutive odd integers.
   Write an equation that represents this relationship.
   
3. Solve the Equation:
   Use algebraic techniques to solve the equation for ‘x’.
   
4. Find the Other Integers:
   Substitute the value of ‘x’ back into the expressions you created in step 1 to find the other consecutive odd integers.
   
5. Check Your Answer:
   Verify that your solution satisfies the conditions of the original word problem.
   

Algebra Worksheets
Practice your skills with the following algebra worksheets:
Printable & Online Algebra Worksheets

Example:
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

Step 2: 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 4: 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

How the solve the integer word problem?

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

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How to find consecutive even and odd numbers given the sums?

Examples:

1. Find three consecutive even numbers whose sum is 84
2. Find four consecutive odd numbers whose sum is 152

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Consecutive Odd Integer Problem

Example:
The product of two consecutive odd integers is 99. What are the numbers?

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Consecutive Odd Integers - Hard

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

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Find 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.

Examples:

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.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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