Common difference of the A.P. `-5, -1, 3, 7, ……` is :

Options

A. `-4`
B. `2`
C. `4`
D. `-5`

Answer

To find the common difference of the arithmetic progression (A.P.) given by the sequence -5, -1, 3, 7, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Terms**:
The first few terms of the A.P. are:
- First term (a) = -5
- Second term (a₂) = -1
- Third term (a₃) = 3
- Fourth term (a₄) = 7

2. **Use the Formula for Common Difference**:
The common difference (d) in an A.P. can be calculated using the formula:
\[ d = a₂ - a₁ \]
where \(a₂\) is the second term and \(a₁\) is the first term.

3. **Substitute the Values**:
Substitute the values of the first and second terms into the formula:
\[ d = -1 - (-5) \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ d = -1 + 5 = 4 \]

5. **Conclusion**:
Therefore, the common difference of the A.P. is:
\[ d = 4 \]

### Final Answer:
The common difference of the A.P. -5, -1, 3, 7 is **4**.

---