Question

Show that the sum of 3 consecutive odd integers is a multiple of 3?

I'm not so sure on how to answer this question, can you please help and show me on how to find it?

Answer 1

any three consecutive numbers:
x , x+1, x+2

their sum
= x + x+1 + x+2
= 3x + 3
= 3(x+1)
since it contains a factor of 3, it must be a multiple of 3

Answer 2

Look at Damon's correct solution to the one above this.

I did not read the question carefully enough and proved that the sum of any 3 consecutive numbers is a multiple of 3.

btw, that is also true for any 3 consecutive even numbers.

Answer 3

it's even easier to see if you call them

x-2, x, x+2

what's the sum?