If the `n^(th)` term of an A.P is `(5n-2)` ,find its Common difference

Answer

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

### Step-by-Step Solution:

1. **Identify the nth term**:
The nth term of the A.P is given as:
\[ a_n = 5n - 2 \]

2. **Find the (n-1)th term**:
To find the (n-1)th term, substitute \( n \) with \( n-1 \):
\[ a_{n-1} = 5(n-1) - 2 = 5n - 5 - 2 = 5n - 7 \]

3. **Calculate the common difference (d)**:
The common difference \( d \) is defined as the difference between the nth term and the (n-1)th term:
\[ d = a_n - a_{n-1} \]
Substituting the values we found:
\[ d = (5n - 2) - (5n - 7) \]

4. **Simplify the expression**:
Now, simplify the expression:
\[ d = 5n - 2 - 5n + 7 \]
The \( 5n \) terms cancel out:
\[ d = -2 + 7 = 5 \]

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