The Fast Way to Find 3 Consecutive Numbers with a Given Sum

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.

Step-by-Step Method:

1. Define the Consecutive Numbers: Let's denote the three consecutive integers as $x-\mathrm{1\; , }$$x$ , and $x+1$ . Here, $x$ represents the middle number in the sequence.

2. Set Up the Equation: The sum of these three numbers can be written as:

   $$(x-1) + x + (x+1)$$ 

3. Simplify the Equation: Simplify the left side of the equation by combining like terms:

   $$(x-1) + x + (x+1) = 3x$$ 
   

   So, the equation becomes:

   $$3x = \text{Given Sum}$$ 

4. Solve for $x$ : To find the value of $x$ , divide the given sum by 3:

   $$x = \frac{\text{Given Sum}}{3}$$

5.  Determine the Three Consecutive Numbers: Once $x$ is found, the three consecutive integers are:

   $$x-1, \quad x, \quad x+1$$ 

Example:

Suppose we want to find three consecutive integers whose sum is 48.

1. Set Up the Equation:

   $$3x = 48$$ 

2. Solve for $x$ :

   $$x = \frac{48}{3} = 16$$ 

3. Find the Consecutive Numbers: The three consecutive numbers are:

   $$16-1 = 15, \quad 16, \quad 16+1 = 17$$ 

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.

Radarhot.com

Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt.