The sum of first 20 odd natural numbers is

Options

A. 100
B. 210
C. 400
D. 420

Explanation

To find the sum of the first 20 odd natural numbers, we can use the formula for the sum of an arithmetic progression (AP). The odd natural numbers form an arithmetic sequence where the first term \( a = 1 \) and the common difference \( d = 2 \).

### Step-by-step Solution:

1. **Identify the parameters**:
- The first term \( a = 1 \)
- The number of terms \( n = 20 \)
- The common difference \( d = 2 \)

2. **Use the formula for the sum of the first \( n \) terms of an arithmetic progression**:
The formula is given by:
\[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \]
where \( S_n \) is the sum of the first \( n \) terms.

3. **Substitute the values into the formula**:
\[ S_{20} = \frac{20}{2} \times (2 \times 1 + (20 - 1) \times 2) \]

4. **Calculate \( S_{20} \)**:
- First, calculate \( \frac{20}{2} = 10 \).
- Next, calculate \( 2 \times 1 = 2 \).
- Then, calculate \( (20 - 1) \times 2 = 19 \times 2 = 38 \).
- Now, add these results: \( 2 + 38 = 40 \).
- Finally, multiply by 10: \( 10 \times 40 = 400 \).

5. **Conclusion**:
The sum of the first 20 odd natural numbers is \( 400 \).