The average of the first 10 positive even numbers is?

Concept: For a set of evenly spaced (arithmetic) numbers, the average equals the mean of the first and last terms — Average = (first term + last term) / 2. Equivalently, the sum of the first n even natural numbers (2, 4, 6, …, 2n) is n(n + 1), so their average is n(n + 1) / n = n + 1.

1. List the first 10 even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

2. Add all ten numbers: 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110.

3. Divide the sum by the count of numbers: Average = 110 / 10 = 11.

Cross-check: Using the first-and-last-term shortcut, Average = (2 + 20) / 2 = 22 / 2 = 11 — the same result.

So the average of the first 10 even numbers is 11.