More Lessons for Algebra
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?
Step 1: Assign variables :
Let x = least integer
x + 1 = middle integer
Sentence: The sum of the least and greatest is 60.
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.
(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.
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