Question

How do you Find the three consecutive even numbers such that the sum of the first and the third is twice the second?

Answer 1

True for any three consecutive even numbers.

Explanation:

Even numbers are of the form `n=2k`; `k in ZZ` (`k` is an integer).

Let's consider three consecutive even numbers `2k`, `2(k + 1)`, and `2(k + 2)`.

"The sum of the first and the third is twice the second".

Algebraically, we would express this as:

`Rightarrow 2k + 2(k + 2) = 2 cdot 2(k + 1) = 4 (k + 1)`

Expanding out the parentheses:

`Rightarrow 2k + 2k + 4 = 4k + 4`

Collecting like terms:

`Rightarrow 4k + 4 = 4k + 4`

`Rightarrow 0 = 0`

Both sides of the equation reach an equality.

This means that, for any three consecutive even numbers, the sum of the first and the third is always twice the second.