Average of odd numbers up to 100: What is the average of all odd numbers from 1 to 99 (i.e., all odd numbers up to 100)?

Introduction / Context:The average of an arithmetic sequence equals the mean of its first and last terms.

Given Data / Assumptions:

• Odd numbers from 1 to 99 form an arithmetic sequence with common difference 2
• First term = 1, last term = 99

Concept / Approach:Average of any arithmetic sequence = (first + last) / 2. The count (50 odds) is not necessary to compute the average itself.

Step-by-Step Solution:Average = (1 + 99) / 2 = 100 / 2 = 50

Verification / Alternative check:Pair 1 with 99, 3 with 97, etc.; each pair averages to 50 and there are equal pairs, confirming 50.

Why Other Options Are Wrong:51, 49.5, 49, 50.5 are inconsistent with the symmetry of the odd sequence around 50.

Common Pitfalls:Confusing with the average of integers 1 to 100 (50.5) instead of odd numbers 1 to 99 (50).

Final Answer:50