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?
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
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
The following video shows how to find consecutive even and odd numbers given the sums.
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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