If gerneral term of an A.P. is 2n + 5 , then its
common difference is

Options

A. 2
B. 3
C. 5
D. 7

Answer

To find the common difference of the arithmetic progression (A.P.) given by the general term \( a_n = 2n + 5 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the General Term**:
The general term of the A.P. is given as:
\[ a_n = 2n + 5 \]

2. **Calculate the First Term**:
To find the first term \( a_1 \), substitute \( n = 1 \) into the general term:
\[ a_1 = 2(1) + 5 = 2 + 5 = 7 \]

3. **Calculate the Second Term**:
To find the second term \( a_2 \), substitute \( n = 2 \) into the general term:
\[ a_2 = 2(2) + 5 = 4 + 5 = 9 \]

4. **Find the Common Difference**:
The common difference \( d \) in an A.P. is calculated as:
\[ d = a_2 - a_1 \]
Substituting the values we found:
\[ d = 9 - 7 = 2 \]

5. **Conclusion**:
Therefore, the common difference of the A.P. is:
\[ d = 2 \]