What is the average of all numbers between 11 and 80 (inclusive bounds not required) that are divisible by 6?

Introduction: Finding the average of equally spaced numbers (an arithmetic progression) uses a simple midpoint property. For any AP, the average of all terms equals the average of the first and last term.

Given Data / Assumptions: Multiples of 6 in the open interval (11, 80): 12, 18, ..., 78. First term a = 12, last term l = 78.

Concept / Approach: For an AP, Average = (first + last) / 2. No need to count terms explicitly if first and last are known.

Step-by-Step Solution: Average = (12 + 78) / 2 = 90 / 2 = 45.

Verification / Alternative check: The list is symmetric around 45: pairs (12,78), (18,72), ..., each summing to 90, confirming the average 45.

Why Other Options Are Wrong: 46, 47, 44, 48: Do not equal the AP mean (12 + 78)/2.

Common Pitfalls: Enumerating all terms unnecessarily or mistakenly including 6 or 84. Respect the interval and the divisibility rule.

Final Answer: The required average is 45.