In the number series 28, 33, 31, 36, 34, 29, one term does not follow the same alternating pattern of operations as the others. Which term in the series is incorrect?

Introduction / Context:
Number series questions appear frequently in arithmetic reasoning tests. The objective is to identify an underlying pattern that generates the terms of the series. Once the pattern is clear, we can detect a term that does not fit or predict the next term. In this question, we must find the wrong number in the series 28, 33, 31, 36, 34, 29 by analysing the sequence of operations from one term to the next.

Given Data / Assumptions:

• The given series is 28, 33, 31, 36, 34, 29.
• Each term is generated from the previous term by a simple arithmetic operation.
• The operations may follow an alternating pattern.
• Exactly one term is inconsistent with the underlying rule.

Concept / Approach:
A natural way to approach such questions is to examine the differences between consecutive terms. Alternating patterns such as plus and minus or increasing and decreasing differences are common. Once we compute these differences, we can look for a simple rule such as add 5, subtract 2 repeatedly, or similar. The term that breaks this pattern will be identified as the wrong number.

Step-by-Step Solution:
Step 1: Compute the difference between 33 and 28: 33 − 28 = 5. Step 2: Compute the difference between 31 and 33: 31 − 33 = −2. Step 3: Compute the difference between 36 and 31: 36 − 31 = 5. Step 4: Compute the difference between 34 and 36: 34 − 36 = −2. Step 5: Compute the difference between 29 and 34: 29 − 34 = −5. Step 6: We observe an alternating pattern of +5, −2, +5, −2, then suddenly −5. The expected continuation would be +5, −2, +5, −2, +5, and so on. Step 7: If we continue the established pattern, the term after 34 should be 34 + 5 = 39, not 29. Therefore, 29 is the wrong term in the series.

Verification / Alternative check:
We can reconstruct the intended series by starting from 28 and repeatedly applying the pattern add 5, subtract 2. Starting from 28, we get: 28 + 5 = 33, 33 − 2 = 31, 31 + 5 = 36, 36 − 2 = 34, 34 + 5 = 39. This reconstructed sequence 28, 33, 31, 36, 34, 39 matches the pattern perfectly and confirms that the originally given last term 29 is inconsistent.

Why Other Options Are Wrong:
33: Fits the pattern as 28 + 5.
36: Fits the pattern as 31 + 5.
34: Fits the pattern as 36 − 2.
None of the above: This would mean no term is wrong, which is not correct because the pattern clearly demands 39 instead of 29 at the end.

Common Pitfalls:
Many test takers misread the pattern as add 5, subtract something else, or they may not notice that the differences themselves are alternating. Another mistake is to attempt complicated formulas when a simple difference analysis is enough. To avoid such errors, always start with the simplest difference pattern and check whether it holds consistently across the entire series.

Final Answer:
The only term that breaks the alternating pattern of +5 and −2 is 29, so it is the wrong number in the series.