The sum of three consecutive even numbers is divisible by _________

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Solution

The correct option is A 6
The correct answer is Option (a)
Let three consecutive even numbers be:
2n, 2n + 2 and2n+ 4.
Their sum is: 2n+2n+2+2n+ 4

=(2n + 2n + 2n) + (2 + 4)

[Collecting like terms]
= 6n + 6 = 6(n +1) [Taking 6 common]
= 6k
Where k = n +1
So it is divisible by 6.
$∴$ The sum of three consecutive even numbers is divisible by 6.

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