Let x1 x2 x3 x4 be a 2consecutive sequence Show that its sum

Let x1, x2, x3, x4 be a 2-consecutive sequence. Show that its sum (e.g. x1 + x2 + x3 + x4) is divisible by 4. Prove using a Direct proof

There are two cases:

1) x1 mod 4 is 2. So x2 mod 4 is 0 and x3 mod 4 is 2 and x4 mod 4 is 0. So the total of x1+x2+x3+x4 mod 4 is (4 mod 4) which is 0.

2) x1 mod 4 is 0. So x2 mod 4 is 2 and x3 mod 4 is 0 and x4 mod 4 is 2. So the total of x1+x2+x3+x4 mod 4 is (4 mod 4) which is 0.

3) x1 mod 4 is 1. So x2 mod 4 is 3 and x3 mod 4 is 1 and x4 mod 4 is 3. So the total of x1+x2+x3+x4 mod 4 is (8 mod 4) which is 0.

4) x1 mod 4 is 3. So x2 mod 4 is 1 and x3 mod 4 is 3 and x4 mod 4 is 1. So the total of x1+x2+x3+x4 mod 4 is (8 mod 4) which is 0.

Therefore x+x2+X3+x4 is always divisible by 4.