Question

The sum of 6 consecutive integers is 204

Answer 1

Ok so we know that the integers are consecutive, so they only have a difference of one between them.

We also know that they add up to 204.

If we make the smallest number be "n";

n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) = 204

If we simplfy the right hand side,
6n + 15 = 204
6n = 189
So n = 31.5

However, n must be a whole number, which means that the original value, 204 must not be right.

Maybe double check the question you were given

Hope this helped in some way so you could at least understand the concept.

Answer 2

Denote the average of the six numbers as n. This will be an even number and the six odd numbers are:

n−5,n−3,n−1,n+1,n+3,n+5

Then:

204=(n−5)+(n−3)+(n−1)+(n+1)+(n+3)+(n+5)=6n

Divide both ends by 6 and transpose to find:

n=2046=34

So the six odd numbers are:

29,31,33,35,37,39