Answer: As printed, it is not an A.P.
Differences: \(\frac{5}{2} - 2 = \frac{1}{2}\), \(3 - \frac{5}{2} = \frac{1}{2}\), but \(\frac{7}{3} - 3 = -\frac{2}{3}\).
The difference is not constant, so the sequence is not an A.P.
Note: the textbook answer key says "Yes, \(d = \frac{1}{2}\)", which fits if the fourth term is \(\frac{7}{2}\) (a likely misprint): then 2, \(\frac{5}{2}\), 3, \(\frac{7}{2}\) is an A.P. with \(d = \frac{1}{2}\).