Find out the wrong term in the series: 125, 126, 124, 127, 123, 129.

Introduction / Context:
This question asks you to spot the wrong term in a series constructed by alternately adding and subtracting consecutive natural numbers. Such alternating plus minus patterns are very common and can be recognised by examining the successive differences carefully.

Given Data / Assumptions:

• Series: 125, 126, 124, 127, 123, 129.
• Exactly one term is incorrect.
• The pattern likely involves adding and subtracting small integers in order.

Concept / Approach:
We compute the differences between consecutive terms and then see if these differences can be interpreted as +1, -2, +3, -4, +5, ... or a similar scheme. If one step does not fit this pattern, the associated term is almost certainly the wrong one. Alternating sign sequences are simple but easy to misread without systematic calculation.

Step-by-Step Solution:
Step 1: Compute differences. 126 - 125 = +1. 124 - 126 = -2. 127 - 124 = +3. 123 - 127 = -4. 129 - 123 = +6. Step 2: The differences are +1, -2, +3, -4, +6. Step 3: Notice that the natural pattern appears to be +1, -2, +3, -4, +5, ... where the absolute values 1, 2, 3, 4, 5 are consecutive integers and the signs alternate. Step 4: According to this rule, after -4 the next difference should be +5, not +6. Step 5: Apply the correct difference to the preceding term: 123 + 5 = 128. Step 6: Therefore, the proper last term should be 128, indicating that the given last term 129 is wrong.

Verification / Alternative check:
Replace 129 with 128 and recompute the differences: 126 - 125 = +1, 124 - 126 = -2, 127 - 124 = +3, 123 - 127 = -4, 128 - 123 = +5. Now the absolute values of the differences are 1, 2, 3, 4, 5 in order, and the signs alternate +, -, +, -, +. This is a neat, textbook example of an alternating plus minus pattern based on consecutive integers, confirming the correctness of our adjustment.

Why Other Options Are Wrong:
If we remove 125, 126, 124, 127, or 123 instead, there is no simple way to reconstruct the series with alternating differences that are consecutive integers. These values are all integral to maintaining the orderly progression until the final step. Changing any of them introduces more than one irregular difference, which is highly unlikely in a single error series question.

Common Pitfalls:
Some learners only compute the first two or three differences and miss the emerging pattern. Others expect the differences themselves to be symmetric around zero without noticing the clear sequence 1, 2, 3, 4, 5 in the magnitudes. Always compute all the differences and look carefully at absolute values as well as signs.

Final Answer:
The term that does not fit the alternating pattern and is therefore wrong is 129.