Question

Prove that the sum of three consecutive even number is always a multiple of 6​

Answer 1

Step-by-step explanation:

If you see the any three consecutive numbers, you can figure out atleast one of them is divisible by 6. We can use mathematical induction for proving it mathematically. For a number to be divisible by 6, it should be divisible by 2 and 3. Since all are even numbers, the number will be divisible by 2.

Answer 2

It is true that the sum of three consecutive even number is always a multiple of 6​. Proved using mathematical induction.

Step-by-step explanation:

To proof:

The sum of three consecutive even number is always a multiple of 6​.

Solution:

Let the three consecutive even numbers be $2n$, $(2n+2)$ and $(2n+4)$.

After adding them, we have:  

$2n+(2n+2)+(2n+4)\\=6n+6\\=6(n+1)$

Hence, it is proved that it is a multiple of 6.