The arithmetic mean of first 11 natural numbers is

### Concept & Formula Natural numbers form an Arithmetic Progression (AP) with a common difference of 1. The average of any AP is simply the midpoint between the first and last terms. $$Average = \frac{First\ Term + Last\ Term}{2}$$ ### Step-by-Step Solution * **Given:** We need the arithmetic mean of the first 11 natural numbers. * **Deduction:** The series is 1, 2, 3, ..., 11. * The first term is 1, and the last term is 11. * **Calculation:** Apply the AP average formula. * $Average = \frac{1 + 11}{2}$ * $Average = \frac{12}{2} = 6.0$. ### Exam Strategy & Shortcut For the first $n$ natural numbers, the mean is always $\frac{n + 1}{2}$. Substitute $n = 11$ to get $\frac{12}{2} = 6$. This is a fundamental property to memorize for rapid solving. ### Common Pitfall A common mistake is starting the sequence from 0 (whole numbers) instead of 1 (natural numbers), which would incorrectly shift the average to 5. Natural numbers strictly begin at 1. ### Final Answer **Therefore, the correct answer is 6.0.**