3 digit numbers whose one digit is the average of the other two

Question: How many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two?

How can this be solved with an arithmetic sequence?

I can see that any two digits must be same parity to produce the even sum. Also any two of the digits must be divisible by $2$. if $\overline{abc}$ is the digit, $a+b=2c$ and doing that for all three digits gives three equations. Thats as far as I can get.