In the following number series, exactly one term does not fit the underlying pattern: 2, 3, 4, 4, 6, 8, 9, 12, 16. Identify which term is wrong.

Introduction / Context:
This question asks us to find a single wrong term in a number series. Such problems generally involve splitting the series into sub series or identifying patterns in the gaps between terms. The challenge is to see the hidden structure that explains every correct term and exposes the incorrect one.

Given Data / Assumptions:

• Series: 2, 3, 4, 4, 6, 8, 9, 12, 16.
• Exactly one term is wrong, and all other terms follow a consistent pattern.
• We assume simple arithmetic patterns such as separate interleaved sequences.

Concept / Approach:
Many such series are formed by combining two or more smaller sequences. One reliable approach is to pick every third term or every second term and see if these subsequences follow a simple rule. If a particular value violates that rule, it is the wrong term. Here we will try grouping terms based on their position in the series.

Step-by-Step Solution:
1. Consider the terms at positions 1, 4, and 7: 2, 4, 9. 2. If this subsequence is correct, it should follow a simple pattern. Notice 2 doubled gives 4. 3. Continuing the same logic, 4 doubled should give 8, but the term present is 9. So 9 does not fit the pattern of doubling. 4. Now look at the terms at positions 2, 5, and 8: 3, 6, 12. Each term is double the previous (3 * 2 = 6, 6 * 2 = 12). 5. Next, observe the terms at positions 3, 6, and 9: 4, 8, 16. Again, each term is double the previous (4 * 2 = 8, 8 * 2 = 16). 6. So there are three subsequences, each formed by repeatedly multiplying by 2. 7. The only term breaking this beautiful doubling structure is 9, which should have been 8 to continue 2, 4, 8.

Verification / Alternative check:
Subsequence 1 (positions 1, 4, 7): 2, 4, 9 should be 2, 4, 8 under repeated multiplication by 2. Subsequence 2 (positions 2, 5, 8): 3, 6, 12 strictly follows the rule n_k+1 = 2 * n_k. Subsequence 3 (positions 3, 6, 9): 4, 8, 16 also strictly follows doubling. If we replace 9 with 8, the entire combined series becomes consistent and well structured. Therefore the series logic confirms that 9 is the wrong term.

Why Other Options Are Wrong:

• 12: If 12 were wrong, the subsequence 3, 6, 12 would break, but that subsequence currently fits a perfect doubling pattern.
• 16: 4, 8, 16 is a perfect doubling sequence, so 16 is consistent.
• 8: Appears in both 4, 8, 16 and as a neighbour in the main sequence, and it fits all observed regularities.

Common Pitfalls:
One common mistake is to focus only on consecutive differences: 1, 1, 0, 2, 2, 1, 3, 4 which look irregular and do not immediately reveal the logic. Without splitting the series into subsequences, it is hard to notice the repeated pattern of doubling. Students may then guess randomly or declare more than one term as suspicious, which is not allowed. Always try grouping terms by position (for example every second or third term) in such questions.

Final Answer:
The wrong term in the series is 9.