What is the sum of two consecutive even numbers

Mathematics
1

what is the sum of two consecutive even numbers

2

What is the sum of two consecutive even numbers?

Answer:

To solve this problem, we will first define what consecutive even numbers are and then find their sum step by step.

Step 1: Understand Consecutive Even Numbers

Consecutive even numbers are even numbers that follow one another in sequence. For example, 2 and 4, 8 and 10, 14 and 16, etc. In general, if you have an even number n, the next consecutive even number is n + 2. This is because even numbers differ by 2.

Step 2: Define the Even Numbers

Let’s define the two consecutive even numbers as:

  • First even number: ( n )
  • Second consecutive even number: ( n + 2 )

Here, n is an even integer.

Step 3: Calculate the Sum

The sum of these two consecutive even numbers can be calculated as follows:

  1. First, write down the expression for the sum:

    \text{Sum} = n + (n + 2)

  2. Simplify the expression:

    \text{Sum} = n + n + 2

  3. Combine like terms:

    \text{Sum} = 2n + 2

This expression, (2n + 2), represents the sum of two consecutive even numbers.

Step 4: Analyze the Result

Let’s analyze the expression (2n + 2):

  • The term (2n) is always an even number because any number multiplied by 2 is even.
  • The additional 2 is also even, so the whole expression (2n + 2) is indeed even.
  • The result is a multiple of 2, specifically written as (2(n+1)), suggesting that the sum of two consecutive even numbers is always divisible by 2 and remains an even number.

Final Answer:

The sum of two consecutive even numbers is given by the formula (2n + 2), where n is the first even number. This sum will always be even and is equal to 2(n + 1).