What will be the sum of first 20 natural number ?

Options

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

Answer

To find the sum of the first 20 natural numbers, we can use the formula for the sum of an arithmetic progression (AP). The natural numbers form an arithmetic sequence where the first term \( A = 1 \), the common difference \( D = 1 \), and the number of terms \( n = 20 \).

### Step-by-Step Solution:

1. **Identify the parameters**:
- First term \( A = 1 \)
- Number of terms \( n = 20 \)
- Common difference \( D = 1 \) (since the difference between consecutive natural numbers is 1)

2. **Use the formula for the sum of the first \( n \) terms of an AP**:
\[ S_n = \frac{n}{2} \times (2A + (n - 1)D) \]
Here, \( S_n \) is the sum of the first \( n \) terms.

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

4. **Calculate**:
- First, calculate \( \frac{20}{2} = 10 \).
- Next, calculate \( 2 \times 1 = 2 \).
- Then, calculate \( (20 - 1) \times 1 = 19 \).
- Now, substitute these values back into the equation:
\[ S_{20} = 10 \times (2 + 19) \]
- Simplifying further:
\[ S_{20} = 10 \times 21 = 210 \]

5. **Final Answer**:
The sum of the first 20 natural numbers is \( 210 \).