If this is an arithmetic sequence there will be a fixed common difference.
The difference between the first and second terms is 5y+3-4y=y+3.
The difference between the second and third terms is 7y+1-(5y+3)=2y-2.
Since the difference is constant, 2y-2=y+3, y=5.
When y=5 the series becomes 20, 28, 36, and the common difference is 8.
However, 250 does not appear in the series:
20, 28, 36, ..., 244, 252.