The average of the first 100 positive integers is

### Concept & Formula The set of positive integers starting from 1 forms an Arithmetic Progression (AP) with a common difference of 1. The average of the first $n$ natural numbers (positive integers) can be found using a direct formula. $$Average = \frac{n + 1}{2}$$ ### Step-by-Step Solution * **Given:** We need the average of the first 100 positive integers. * **Deduction:** The sequence is 1, 2, 3, ..., 100. * Here, the total number of terms $n$ is 100. * **Calculation:** Plug $n = 100$ into the standard AP average formula. * $Average = \frac{100 + 1}{2}$ * $Average = \frac{101}{2}$ * $Average = 50.5$ ### Exam Strategy & Shortcut For any sequence with a constant difference (like consecutive integers), the average is simply the midpoint between the first and last term. First term is 1, last term is 100. Average is $(1 + 100) / 2 = 50.5$. Memorize this property for instant answers. ### Common Pitfall Confusing "positive integers" with "whole numbers." Whole numbers start at 0, which would make the first 100 numbers range from 0 to 99, changing the average to 49.5. Positive integers strictly begin at 1. ### Final Answer **Therefore, the correct answer is 50.5.**