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This problem trains for: SAT-I, AMC-8, GMAT.

Choose three consecutive perfect squares greater than 1 on the x-axis. The values of:

equation

at these three points:

Let the three consecutive perfect squares be:

equation

The values of f at these points are:

equation

These values form an arithmetic sequence with common difference 1.

As for any arithmetic sequence, the middle term is the average of its neighbors.

Only I and IV are true.