The sum of 5 consecutive even numbers is 180 what is the first number in the sequence

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.