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

1 Answer
Mar 14, 2018

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.