There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats and so on . How many seats are there in the 21st row ?

Explanation

To find the number of seats in the 21st row of the auditorium, we can use the formula for the nth term of an arithmetic progression (AP).

### Step-by-Step Solution:

1. **Identify the first term (A) and the common difference (D)**:
- The first row has 20 seats, so the first term \( A = 20 \).
- The second row has 22 seats, and the third row has 24 seats. The difference between consecutive rows is \( 22 - 20 = 2 \) and \( 24 - 22 = 2 \). Thus, the common difference \( D = 2 \).

2. **Use the formula for the nth term of an AP**:
- The formula for the nth term \( T_n \) of an arithmetic progression is given by:
\[ T_n = A + (n - 1)D \]
- Here, we need to find the 21st term, so \( n = 21 \).

3. **Substitute the values into the formula**:
- Substitute \( A = 20 \), \( D = 2 \), and \( n = 21 \) into the formula:
\[ T_{21} = 20 + (21 - 1) \cdot 2 \]

4. **Calculate the value**:
- Simplify the expression:
\[ T_{21} = 20 + 20 \cdot 2 \]
\[ T_{21} = 20 + 40 \]
\[ T_{21} = 60 \]

5. **Conclusion**:
- Therefore, the number of seats in the 21st row is **60**.