The Fast Way to Find 3 Consecutive Numbers with a Given Sum
Finding three consecutive numbers that sum to a given value is a common problem in mathematics, often encountered in various contexts such as arithmetic sequences and algebra. This problem can be efficiently solved using algebraic methods. Here, we will explore a quick and systematic way to find three consecutive integers whose sum equals a given number.
Finding three consecutive numbers that sum to a given value is a common problem in mathematics, often encountered in various contexts such as arithmetic sequences and algebra. This problem can be efficiently solved using algebraic methods. Here, we will explore a quick and systematic way to find three consecutive integers whose sum equals a given number.
Step-by-Step Method:
Define the Consecutive Numbers:
Let's denote the three consecutive integers as , and . Here, represents the middle number in the sequence.
Set Up the Equation:
The sum of these three numbers can be written as:
Simplify the Equation:
Simplify the left side of the equation by combining like terms:
So, the equation becomes:
Solve for :
To find the value of , divide the given sum by 3:
Determine the Three Consecutive Numbers:
Once is found, the three consecutive integers are:
Define the Consecutive Numbers: Let's denote the three consecutive integers as , and . Here, represents the middle number in the sequence.
Set Up the Equation: The sum of these three numbers can be written as:
Simplify the Equation: Simplify the left side of the equation by combining like terms:
So, the equation becomes:
Solve for : To find the value of , divide the given sum by 3:
Determine the Three Consecutive Numbers: Once is found, the three consecutive integers are:
Example:
Suppose we want to find three consecutive integers whose sum is 48.
Set Up the Equation:
Solve for :
Find the Consecutive Numbers:
The three consecutive numbers are:
So, the three consecutive integers whose sum is 48 are 15, 16, and 17.
This method provides a quick and straightforward way to find three consecutive integers with a given sum, leveraging basic algebraic principles to simplify and solve the problem efficiently.
Suppose we want to find three consecutive integers whose sum is 48.
Set Up the Equation:
Solve for :
Find the Consecutive Numbers: The three consecutive numbers are:
So, the three consecutive integers whose sum is 48 are 15, 16, and 17.
This method provides a quick and straightforward way to find three consecutive integers with a given sum, leveraging basic algebraic principles to simplify and solve the problem efficiently.