Question

Find the average of the first hundred numbers?

• A. 50
• B. 50.5
• C. 51
• D. 49.5

Hint:

For any arithmetic progression (evenly spaced sequence), the average is simply the midpoint of the first and last terms:
$\text{Average} = \frac{1 + 100}{2} = 50.5$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The "first hundred numbers" typically refers to the first hundred positive integers (natural numbers) from 1 to 100.
Key Formula or Approach:
The sum of the first $n$ natural numbers is given by: \[ S_n = \frac{n(n + 1)}{2} \] The average is the sum divided by $n$: \[ \text{Average} = \frac{S_n}{n} = \frac{n + 1}{2} \]

Step 2: Detailed Explanation:
Here, $n = 100$.
Substitute $n = 100$ into the average formula: \[ \text{Average} = \frac{100 + 1}{2} = \frac{101}{2} = 50.5 \] Thus, the average of the first hundred natural numbers is 50.5.

Step 3: Final Answer:
The average is 50.5, which corresponds to Option (B).