Math Problem Statement

The sum of [3] consecutive even numbers is [132]. What is the third number in this sequence?

Solution

We are given that the sum of three consecutive even numbers is 132. Let's define the three consecutive even numbers.

Let the middle number be xx. Then, the three consecutive even numbers can be expressed as:

  • The first number: x2x - 2
  • The second number: xx
  • The third number: x+2x + 2

The sum of these three numbers is: (x2)+x+(x+2)(x - 2) + x + (x + 2) Simplifying the expression: (x2)+x+(x+2)=3x(x - 2) + x + (x + 2) = 3x We are told that this sum is 132, so: 3x=1323x = 132 Now, solve for xx: x=1323=44x = \frac{132}{3} = 44 Thus, the middle number is 44. The three consecutive even numbers are:

  • First number: 442=4244 - 2 = 42
  • Second number: 4444
  • Third number: 44+2=4644 + 2 = 46

The third number is 46\boxed{46}.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the sum of 5 consecutive even numbers?
  2. How do we generalize the approach for finding the sum of consecutive even or odd numbers?
  3. If the sum of 3 consecutive odd numbers is given, how would the method change?
  4. Can we solve for consecutive numbers when the sum is odd instead of even?
  5. How would the approach change if the numbers were consecutive prime numbers?

Tip: Always break down the problem by defining variables for the unknowns and use algebraic expressions to simplify the steps.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Sequences
Solving Linear Equations

Formulas

Sum of consecutive even numbers = (x - 2) + x + (x + 2) = 3x

Theorems

Linear equation solving

Suitable Grade Level

Grades 6-8