Question

Take any three consecutive even numbers and add them, say, $2 + 4 + 6 = 12,\,4 + 6 + 8 = 18,\,8 + 10 + 12 = 30$ and so on.

Answer 1

Hint:
For three consecutive even numbers, the numbers which are involved should be divisible by 2, and consecutive means the numbers are next to each other, and should be even numbers.

Complete step by step solution:
Let $x$be a number, then the consecutive even numbers will be in the form of $x,\,x + 2,\,x + 4$, where $x$is also an even number.
For $x = 10$
Consecutive even numbers will be
$
   \Rightarrow x,\,x + 2,\,x + 4 \\
   \Rightarrow 10,\,10 + 2,\,10 + 4 \\
   \Rightarrow 10,\,12,\,14 \\
   \Rightarrow 10 + 12 + 14 = 36 \\
 $
For $x = 12$
Consecutive even numbers will be
$
   \Rightarrow x,\,x + 2,\,x + 4 \\
   \Rightarrow 12,\,12 + 2,\,12 + 4 \\
   \Rightarrow 12,\,14,\,16 \\
   \Rightarrow 12 + 14 + 16 = 42 \\
 $
For $x = 14$
Consecutive even numbers will be
$
   \Rightarrow x,\,x + 2,\,x + 4 \\
   \Rightarrow 14,\,14 + 2,\,14 + 4 \\
   \Rightarrow 14,\,16,\,18 \\
   \Rightarrow 14 + 16 + 18 = 48 \\
 $

So, for every consecutive even number the value of $x$ should also be an even number. When these consecutive even numbers are added the resultant will also be an even number.

Note:
Before any question on consecutive series, try to prepare a form of consecutive series, and substitute the values as mentioned, this becomes easier than finding the series of numbers which satisfies.