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

**Related Pages**

Integers Word Problems

Consecutive Even Integer Problems

Consecutive Integer Word Problems

Consecutive Integers 2

More Algebra Word Problems

Integer worksheets

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.

**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?.

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

**Examples:**

- Find three consecutive even numbers whose sum is 84
- Find four consecutive odd numbers whose sum is 152

**Consecutive Odd Integer Problem**

**Example:**

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

**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.

**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:**

- The sum of three consecutive integers is 657; find the integers.
- The sum of three consecutive odd integers is 597; find the integers.
- The sum of three consecutive even integers is 528; find the integers.

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