Asked by Anonymous

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?

Answers

Answered by Reiny
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
Answered by Reiny
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.
Answered by Steve
it's even easier to see if you call them

x-2, x, x+2

what's the sum?

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