What is the average of first 37 natural numbers?

Options

A. 36
B. 22
C. 19.5
D. 19

Explanation

To find the average of the first 37 natural numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first 37 natural numbers**:
The first 37 natural numbers are 1, 2, 3, ..., 37.

2. **Use the formula for the sum of the first n natural numbers**:
The formula to calculate the sum of the first n natural numbers is:
\[ S_n = \frac{n(n + 1)}{2} \]
where \( n \) is the number of natural numbers.

3. **Substitute \( n = 37 \) into the formula**:
\[ S_{37} = \frac{37(37 + 1)}{2} = \frac{37 \times 38}{2} \]

4. **Calculate the sum**:
\[ S_{37} = \frac{37 \times 38}{2} = \frac{1406}{2} = 703 \]

5. **Calculate the average**:
The average is calculated by dividing the sum by the number of terms:
\[ \text{Average} = \frac{S_{37}}{n} = \frac{703}{37} \]

6. **Perform the division**:
\[ \text{Average} = 19 \]

Thus, the average of the first 37 natural numbers is **19**.