Average of the first nine multiples of 3: Compute the mean of 3, 6, 9, ..., 27.

Introduction / Context:
Multiples of a number form an arithmetic progression. The mean of an arithmetic progression equals the average of its first and last terms.

Given Data / Assumptions:

• Sequence: 3, 6, 9, ..., 27
• Count = 9

Concept / Approach:
Average of an AP = (first + last) / 2. Here, first = 3 and last = 27.

Step-by-Step Solution:

Verification / Alternative check:
The middle term (5th term) in an odd-length AP equals the mean. The 5th term here is 15, confirming the result.

Why Other Options Are Wrong:

• 12.0, 12.5, 18.5, 13.5: do not match AP mean for 3 to 27 with equal spacing of 3.

Common Pitfalls:
Confusing the common difference with the average or miscounting terms.

Final Answer:
15.0