# Consecutive Integer Word Problems

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What are consecutive 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.

How to solve consecutive integer problems?
Example : Consecutive Integer Problem

The sum of the least and greatest of 3 consecutive integers is 60. What are the values of the 3 integers?

Solution:

Step 1: Assign variables :

Let x = least integer
x + 1 = middle integer

• x* + 2 = greatest integer Translate sentence into an equation.

Sentence: The sum of the least and greatest is 60.

Rewrite sentence:

x + (x + 2) = 60 Step 2: Solve the equation

Combine like terms

2x + 2 = 60 Isolate variable x

2x = 58 Step 3: Check your answer

29 + 29 + 2 = 60

The question wants all the 3 consecutive numbers: 29, 30 and 31

Answer: The 3 consecutive numbers are 29, 30 and 31.

The following video shows an example of a consecutive number word problem.
Example:
(1) The sum of 5 consecutive integers is 200, what is the smallest of the 5 integers?
(2) The sum of 7 odd integers is 217, what is the largest of the integers?

How to solve “consecutive integer” word problems?
Example: The sum of three consecutive integers is 24. Find the integers.

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. 