Question

Write the sum of two consecutive even numbers, the greater of which is equal to $2n$.

Answer 1

Finding the sum of two consecutive even numbers:

We want to write the sum of two consecutive even numbers.

Now, both numbers must be consecutive and even. So, the difference between the two numbers will be $2$.

Considering the smaller number is $x$, then the larger number is $x+2$.

Now it is given that the larger number is $2n$, then we have:

$x+2=2n$

Therefore, the smaller number $x$ becomes,

$x=2n-2$

So the two consecutive even numbers are $2n-2$ and $2n$.

Thus, The sum of the two consecutive even numbers can be expressed as,

$$\begin{gathered} =\left(2n-2\right)+2n \\ =4n-2 \end{gathered}$$

Hence, the sum of the two consecutive even numbers is $4n-2$.