Question

The average of the first 100 positive integers is:

• A. 50.5
• B. 51
• C. 515
• D. 495

Hint:

To find the average of the first \( n \) positive integers, use the formula \( \frac{n+1}{2} \), which simplifies the calculation.

Answer 1

The Correct Option is A

Step 1: Understanding the formula for the average of the first \( n \) positive integers.
The sum of the first \( n \) positive integers is given by the formula: \[ \text{Sum of integers} = \frac{n(n+1)}{2}. \] Step 2: Applying the formula for the sum of the first \( n \) integers.
For \( n = 100 \), the sum is: \[ \text{Sum of integers} = \frac{100(100+1)}{2} = \frac{100 \times 101}{2} = 5050. \] Step 3: Finding the average.
The average of the first 100 integers is: \[ \text{Average} = \frac{\text{Sum of integers}}{\text{Number of integers}} = \frac{5050}{100} = 50.5. \] Thus, the average is \( 50.5 \).