First, a even number in general could be written as 2k for any k ( k is any integer number).
Let x_1, x_2, x_3, x_4, x_5 the 5 consecutive even numbers, then,
x_1 + x_2 + x_3 + x_4 + x_5 = 180. But for the first commentary, any of the x_i's are even numbers, so, are of the form 2k_i, but, they are consecutive, think about the sequence: 2,4,6,8,10, we could written as 2(1) + 2 (2) + 2(3) + 2(4) + 2(5), the numbers between (), are the k's and are consecutive, and we could write consecutive numbers as x, x+1, x+1 +1 = x+2, (x+2)+1, etc.
So, for the previous commentary, we rewrite
x_1 + x_2 + x_3 + x_4 + x_5 = 180
as
2k + 2(k+1) + 2(k+2) + 2(k+3) + 2(k+4) = 180
is equivalent to (factorizing 2)
2 [k + k+1 + k+2 +k+3 +k+4 ] = 180
(divide both sides by 2)
[k + k+1 + k+2 +k+3 +k+4 ] = 90
(simplifyng the expression)
5k+10 = 90
(substracting 10 in both sides)
5k = 80
(divide both sides by 5)
k = 16
then, the first number is x_1 = 2k = 2(16) = 32
Now, we can check, the corresponding sequence was
32 + 34 +36 +38 +40 = 180.
