Find the average of the first 50 natural numbers (that is, the numbers from 1 to 50).

Introduction:
This problem asks you to find the average of the first 50 natural numbers. It is a standard arithmetic progression question and demonstrates the formula for the average of a sequence of equally spaced numbers.

Given Data / Assumptions:
We are given the first 50 natural numbers: 1, 2, 3, ..., 50. We need to find the average of these numbers.

Concept / Approach:
The first 50 natural numbers form an arithmetic progression with: First term a = 1. Last term l = 50. For any arithmetic progression, the average (mean) of all terms is: Average = (First term + Last term) / 2. This is because the terms are symmetrically distributed around the midpoint.

Step-by-Step Solution:
Step 1: Identify the first and last terms. First term a = 1. Last term l = 50. Step 2: Use the formula for the average of an arithmetic progression. Average = (a + l) / 2. Average = (1 + 50) / 2. Average = 51 / 2 = 25.5.

Verification / Alternative Check:
If you pair the numbers from the beginning and end, each pair sums to 51: (1, 50), (2, 49), ..., (25, 26). There are 25 such pairs. The average of each pair is 51 / 2 = 25.5, which is also the average of the entire set.

Why Other Options Are Wrong:
25 and 26: These values are close but not equal to the actual computed mean. 26.5 and 24.5: These are further away and do not match the symmetry of the sequence around 25.5.

Common Pitfalls:
Some students try to add all 50 numbers manually, which is time consuming and error prone. Others mistakenly average the first few and assume the same applies to the rest. Using the arithmetic progression formula is the most efficient and accurate way.

Final Answer:
The average of the first 50 natural numbers is 25.5.