The average of first 99 even number is:

Options

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

Answer

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

### Step 1: Identify the first 99 even numbers
The first 99 even numbers are:
2, 4, 6, 8, ..., 198.
These numbers can be expressed in a formula as 2n, where n ranges from 1 to 99.

### Step 2: Calculate the sum of the first 99 even numbers
The sum of the first n even numbers can be calculated using the formula:
\[ \text{Sum} = n(n + 1) \]
Here, n = 99. Therefore, we can calculate the sum as follows:
\[ \text{Sum} = 99 \times (99 + 1) = 99 \times 100 = 9900 \]

### Step 3: Calculate the average
The average is calculated by dividing the sum by the number of terms. In this case, we have 99 even numbers:
\[ \text{Average} = \frac{\text{Sum}}{\text{Number of terms}} = \frac{9900}{99} \]

### Step 4: Simplify the average
Now, we simplify the average:
\[ \text{Average} = \frac{9900}{99} = 100 \]

### Final Answer
The average of the first 99 even numbers is **100**.

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