Question

What is the average of first 101 consecutive odd numbers?

• A. 99
• B. 100
• C. 101
• D. 102

Answer 1

The Correct Option is C

Step 1: Identify the First 101 Odd Numbers

The first 101 odd numbers are: 

1, 3, 5, 7, ..., 201.

The sum of the first n odd numbers is given by the formula:

\[ S_n = n^2 \]

Thus, the sum of the first 101 odd numbers is:

\[ 101^2 = 10201 \]

Step 2: Calculate the Average

The average is given by:

\[ \frac{\text{Sum of terms}}{\text{Number of terms}} \]

Substituting the values:

\[ \frac{10201}{101} = 100 \]

Final Conclusion:

The average of the first 101 odd numbers is 100.