Consecutive Odd Integer Problems

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

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 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 :

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 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.
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.

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