In the sequence 6, 13, 18, 25, 30, 37, 40, which single term is incorrect because it breaks the alternating +7 and +5 pattern?

Introduction / Context:
This question presents an increasing number sequence where the increments follow a simple alternating pattern. Your task is to identify which number does not respect that pattern. Such problems are common in reasoning tests and help you practice working with recurring difference patterns.

Given Data / Assumptions:
The sequence is: 6, 13, 18, 25, 30, 37, 40. We assume there is a regular rule involving additions by fixed numbers (most likely 5 and 7), and exactly one term is wrong.

Concept / Approach:
When a series increases but not by a constant amount, the first step is to check the differences between consecutive terms. If those differences alternate between two values, we can detect that and see which term breaks the pattern. This is the case here.

Step-by-Step Solution:
Step 1: Compute the differences between consecutive terms.6 → 13: difference = +7.13 → 18: difference = +5.18 → 25: difference = +7.25 → 30: difference = +5.30 → 37: difference = +7.37 → 40: difference = +3.Step 2: Notice the pattern: the differences should alternate +7, +5, +7, +5, +7, and so on.Step 3: Following this pattern strictly, after 37 we should add +5, not +3. So the correct next term should be 37 + 5 = 42.Step 4: Therefore, 40 is the only term that does not fit the alternating +7, +5 pattern and is the wrong number in the sequence.

Verification / Alternative check:
Rebuild the sequence using the ideal alternating differences: starting from 6, we get 6 + 7 = 13, 13 + 5 = 18, 18 + 7 = 25, 25 + 5 = 30, 30 + 7 = 37, and 37 + 5 = 42. This yields the correct pattern 6, 13, 18, 25, 30, 37, 42. The given sequence differs only in the last term, which is 40 instead of 42.

Why Other Options Are Wrong:
25, 30 and 37 all fit perfectly into the alternating +7 and +5 structure. Changing any of them would break multiple differences at once and would not restore a clean pattern. Only replacing 40 by 42 keeps the simple alternation intact, so 40 must be the erroneous value.

Common Pitfalls:
Test-takers sometimes look for a single constant difference or try to impose multiplication rules where there are none. Another mistake is to ignore the last step because the change seems small. Even small deviations are important in series questions, so always compute every difference carefully.

Final Answer:
The term that breaks the alternating +7 and +5 pattern is 40.