Which of the following sequences is an A.P.? If they are A.P., find the common difference. `2,(5)/(2),3,(7)/(2)...`

Explanation

To determine if the sequence \(2, \frac{5}{2}, 3, \frac{7}{2}\) is an Arithmetic Progression (A.P.), we need to check if the difference between consecutive terms is constant.

### Step-by-Step Solution:

1. **Identify the Terms**:
- Let \(A_1 = 2\)
- Let \(A_2 = \frac{5}{2}\)
- Let \(A_3 = 3\)
- Let \(A_4 = \frac{7}{2}\)

2. **Calculate the Differences**:
- **First Difference**:
\[ A_2 - A_1 = \frac{5}{2} - 2 = \frac{5}{2} - \frac{4}{2} = \frac{1}{2} \]
- **Second Difference**:
\[ A_3 - A_2 = 3 - \frac{5}{2} = \frac{6}{2} - \frac{5}{2} = \frac{1}{2} \]
- **Third Difference**:
\[ A_4 - A_3 = \frac{7}{2} - 3 = \frac{7}{2} - \frac{6}{2} = \frac{1}{2} \]

3. **Check for Constant Difference**:
- We found:
\[ A_2 - A_1 = \frac{1}{2}, \quad A_3 - A_2 = \frac{1}{2}, \quad A_4 - A_3 = \frac{1}{2} \]
- Since all differences are equal, the sequence is indeed an A.P.

4. **Find the Common Difference**:
- The common difference \(D\) is:
\[ D = \frac{1}{2} \]

### Conclusion:
The sequence \(2, \frac{5}{2}, 3, \frac{7}{2}\) is an Arithmetic Progression, and the common difference is \(\frac{1}{2}\).