What is the average of all natural numbers from 21 to 39 inclusive?

Introduction / Context:
This question is about finding the average of a sequence of consecutive natural numbers. The numbers run from 21 to 39 inclusive, and you must compute their arithmetic mean. This is a basic concept in aptitude tests and helps build familiarity with arithmetic progressions and averages.

Given Data / Assumptions:
- We are dealing with natural numbers from 21 to 39 inclusive.
- The numbers form an arithmetic progression with common difference 1.
- We must find the arithmetic mean of all these numbers.

Concept / Approach:
For any arithmetic progression with equally spaced terms, the average or arithmetic mean is simply the mean of the first and last terms. This works because the sequence is symmetric: the smallest and largest terms balance each other around the center, and similarly for the inner pairs. Therefore we do not need to list or add all terms; we can use the simple formula average = (first + last) / 2.

Step-by-Step Solution:
Step 1: Identify the first term of the sequence: 21.Step 2: Identify the last term of the sequence: 39.Step 3: Use the formula for the average of an arithmetic progression: average = (first term + last term) / 2.Step 4: Substitute the values: average = (21 + 39) / 2.Step 5: Compute the sum: 21 + 39 = 60.Step 6: Divide by 2: 60 / 2 = 30.Step 7: Therefore the required average is 30.

Verification / Alternative check:
If you want to check manually, you can write the numbers as pairs that add up to 60: (21, 39), (22, 38), (23, 37), (24, 36), (25, 35), (26, 34), (27, 33), (28, 32), (29, 31). The middle term is 30, and for each pair the average is 30. Because all pairs and the central value 30 balance around 30, the overall average is also 30. This confirms the formula based method.

Why Other Options Are Wrong:
Options like 29, 31 or 28 arise if someone mistakenly counts the number of terms or excludes an endpoint. However, the start and end points 21 and 39 are clearly specified and must be included. Any average different from (21 + 39) / 2 is inconsistent with the structure of this arithmetic progression.

Common Pitfalls:
A common mistake is to add all numbers one by one which is time consuming and prone to arithmetic errors, especially under exam pressure. Another error is to misread the range and stop at 38 instead of 39. Remember that for consecutive numbers, the average is always halfway between the smallest and largest term, which is a very quick and reliable shortcut.

Final Answer:
The average of all natural numbers from 21 to 39 is 30.