I am self-studying Discrete Mathemamatics and I've found the following example (in Portuguese).
Find an arithmetic progression with four terms $(a, a+r,a+2r,a+3r)$ such that the sum of its terms is $16$ and the product is $105$.
The author start by saying that we can assume that its terms are of the form $(y-3r,y-r,y+r,y+3r)$. I didn't understand that statement.
Here's what I did to prove his claim: The sum of its terms is equal to $4a+6r$. Then I put $y=2a+3r$ and then I get the arithmetic progression $(\dfrac{y-3r}{2},\dfrac{y-r}{2},\dfrac{y+r}{2},\dfrac{y+3r}{2})$. As you can see I was not able to prove his claim. What am I doing wrong?
I would appreciate your help.