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The sum of three consecutive numbers is 72. What are the smallest of these numbers?
The smallest of these numbers is 23.
Let’s call the three consecutive numbers x, x+1, and x+2.
According to the given information, the sum of these three numbers is 72:
x + (x+1) + (x+2) = 72
Now, let’s solve for x:
3x + 3 = 72
Subtract 3 from both sides:
3x = 69
Divide both sides by 3:
x = 23
So, the smallest of these numbers is 23.
What are Consecutive Numbers? Properties of Consecutive Numbers
Consecutive numbers are numbers that follow each other in order, with a constant difference between each pair. For example, 1, 2, 3, 4, 5 are consecutive integers because each number is one more than the previous one.
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Properties of consecutive numbers:
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Constant difference: Consecutive numbers always have the same difference between them. For example, in the sequence 1, 2, 3, 4, the difference between each consecutive pair is 1.
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Sum of consecutive integers: The sum of consecutive integers can be found using the formula: Sum = n * (n + 1) / 2, where n is the number of consecutive integers and n + 1 is the largest number in the sequence.
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Product of consecutive integers: The product of consecutive integers is not always predictable unless the sequence starts with 1. For example, the product of the first n consecutive integers starting from 1 is n! (n factorial).
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Properties of consecutive odd or even numbers: Consecutive even or odd numbers have the same properties as consecutive integers but with a difference of 2 between each consecutive pair.
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Median of consecutive numbers: For a set of consecutive integers, the median is the average of the middle two numbers if the total count is even, and if the total count is odd, the median is the middle number.
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Consecutive Prime Numbers: There are sequences of consecutive prime numbers, but these are less predictable and tend to become more sparse as the numbers increase. However, there are conjectures and theorems related to the distribution of prime numbers, such as the Prime Number Theorem, which provides some insights into their behavior.
Understanding consecutive numbers and their properties can be helpful in various mathematical problems, particularly in areas like algebra, number theory, and combinatorics.
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