4y, 5y+3, 7y+1, ...,250 Find the value of y

Question

Consider the following arithmetic sequence

Answer 1

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.