What is the average of all even numbers between 11 and 63 (inclusive of the endpoints if even)?

Introduction: The average of an arithmetic sequence equals the average of its first and last terms. For even numbers in a range, identify the first even and last even within the interval and take their mean.

Given Data / Assumptions:

• Even numbers from 12 to 62 are within 11 to 63.
• Sequence: 12, 14, 16, ..., 62.

Concept / Approach: For any arithmetic progression with constant difference, mean = (first + last) / 2, independent of the number of terms. This avoids summing the entire list.

Step-by-Step Solution:

Verification / Alternative check: The sequence is symmetric around 37: pairs (12,62), (14,60), … all average to 37, confirming the mean.

Why Other Options Are Wrong: 37.5 or 42 would be the mean if endpoints were different; 47 and 36 do not match the symmetric pairing check.

Common Pitfalls: Including 11 or 63 erroneously (both are odd) or trying to count the total terms unnecessarily.

Final Answer: 37