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: 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
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
Step 3: Check your answer13 + 13 + 2 + 13 + 4 = 45
Be careful! The question requires the length of the longest side.
The length of longest = 13 + 4 =17Answer: The length of longest side is 17
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