In the number series 22, 26, 42, 78, 142, 244, find the odd man out by examining the pattern of adding squares of even numbers.

Introduction / Context:
This series 22, 26, 42, 78, 142, 244 is an odd man out question where one term does not fit a neat pattern. The numbers grow faster and faster, so it is natural to suspect that the differences between consecutive terms might involve square numbers or some other non linear structure.

Given Data / Assumptions:
The numbers are:

• 22
• 26
• 42
• 78
• 142
• 244

We assume that the intended pattern uses additions of square numbers, specifically squares of even integers, applied step by step to generate the series.

Concept / Approach:
The first step is to compute the differences between terms. If those differences match a familiar sequence such as squares 2^2, 4^2, 6^2, 8^2, 10^2, then the term that does not match the expected difference can be identified as the odd one out. This technique is widely used in number series problems where growth accelerates.

Step-by-Step Solution:
Step 1: Compute the consecutive differences.26 - 22 = 4, which is 2^2.42 - 26 = 16, which is 4^2.78 - 42 = 36, which is 6^2.142 - 78 = 64, which is 8^2.244 - 142 = 102.Step 2: Compare with the expected pattern. We see the differences 4, 16, 36, 64, which are 2^2, 4^2, 6^2, 8^2.Step 3: The natural continuation of this pattern would be to add 10^2 = 100 after 142.Step 4: So the correct next term should be 142 + 100 = 242, not 244.Step 5: Therefore, 244 does not fit the rule of adding consecutive squares of even numbers and is the odd man out.

Verification / Alternative check:
We can reconstruct the intended sequence: starting from 22, we add 2^2 to get 26, then add 4^2 to get 42, then add 6^2 to get 78, then add 8^2 to get 142, and finally we would add 10^2 to get 242. The given term 244 breaks this otherwise smooth pattern, confirming that it must be the incorrect or odd term.

Why Other Options Are Wrong:
The terms 142, 78 and 42 each fit perfectly into the pattern of consecutive even squares. If we removed any of them, we could not maintain the 2^2, 4^2, 6^2, 8^2, 10^2 difference structure. Only by replacing 244 with 242 does the pattern remain intact, so 244 is the only term that can reasonably be called the odd one out.

Common Pitfalls:
Some test-takers focus only on the rough size of the jumps and miss the exact square structure. Others may try to fit a single multiplicative factor, which does not hold because the ratios between terms are not constant. Looking at differences and asking whether they are squares or cubes is a key technique for solving many such questions.

Final Answer:
The number that does not follow the pattern of adding squares of even numbers is 244.