The average of first 99 natural even numbers is :

Options

A. 9999
B. 100
C. 9801
D. 9009

Answer

To find the average of the first 99 natural even numbers, we can follow these steps:

### Step 1: Identify the first 99 natural even numbers
The first natural even numbers are:
2, 4, 6, 8, ..., up to the 99th even number.

### Step 2: Determine the formula for the nth even number
The nth even number can be expressed as:
\[ \text{nth even number} = 2n \]
So, the 99th even number is:
\[ 2 \times 99 = 198 \]

### Step 3: Calculate the sum of the first 99 natural even numbers
The sum of the first n even numbers can be calculated using the formula:
\[ S_n = n/2 \times (a + l) \]
where:
- \( n \) is the number of terms (99),
- \( a \) is the first term (2),
- \( l \) is the last term (198).

Substituting the values:
\[ S_{99} = \frac{99}{2} \times (2 + 198) \]
\[ S_{99} = \frac{99}{2} \times 200 \]
\[ S_{99} = 99 \times 100 = 9900 \]

### Step 4: Calculate the average
The average is given by the formula:
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
So, substituting the values we found:
\[ \text{Average} = \frac{9900}{99} = 100 \]

### Conclusion
The average of the first 99 natural even numbers is **100**.

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