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

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Answer 1 · 2018-03-14T21:01:51

True for any three consecutive even numbers.

Even numbers are of the form $n = 2 k$ $n=2k$ ; $k in ZZ$ ( $k$ 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.