Find the wrong term in the number series 1, 5, 9, 15, 25, 37, 49.

Introduction / Context:

This question asks you to detect the incorrect term in an otherwise regular number series. Instead of filling a missing value, you must identify which given value breaks the pattern. Such problems are very common in reasoning tests because they require not only seeing the rule that generates the series but also checking every term against that rule to see which one does not fit.

Given Data / Assumptions:

• The series provided is 1, 5, 9, 15, 25, 37, 49.
• Exactly one of these terms is wrong; the rest form a consistent pattern.
• The pattern likely relates to differences between consecutive terms.
• We must find the offending term that does not conform to the common rule.

Concept / Approach:

For wrong term questions, it is usually easier to first assume that the series is correct and try to deduce a rule. If that rule works for most transitions but fails at a particular value, that value is the wrong term. Here, the numbers increase moderately, suggesting that the series might be based on adding numbers that themselves follow a pattern, such as in pairs or groups. Recognizing repetition in the differences can reveal the intended structure, and any deviation immediately highlights the incorrect term.

Step-by-Step Solution:

Step 1: Compute differences between terms: 1 to 5 is plus 4, 5 to 9 is plus 4, 9 to 15 is plus 6, 15 to 25 is plus 10, 25 to 37 is plus 12, 37 to 49 is plus 12. Step 2: The differences are 4, 4, 6, 10, 12, 12. Step 3: A reasonable intended pattern is to have equal differences in pairs that themselves increase: plus 4, plus 4, plus 8, plus 8, plus 12, plus 12. Step 4: Based on this intended rule, the correct sequence would be 1, 5, 9, 17, 25, 37, 49, where after adding 4 twice, we add 8 twice, then 12 twice. Step 5: Comparing the intended correct sequence with the given one, only the third term after 9 is different: the series has 15 instead of 17, so 15 must be the wrong term.

Verification / Alternative check:

Reconstruct the ideal series using the rule of equal differences in pairs. Start from 1: add 4 to get 5, add 4 to get 9. Then add 8 to get 17, add 8 to get 25. Next add 12 to get 37, add 12 to get 49. The fully consistent series is therefore 1, 5, 9, 17, 25, 37, 49. In this correct pattern, every pair of successive differences is equal and then increases by 4 for the next pair. The given series matches this pattern at all positions except at 15, confirming that 15 is the misplaced term.

Why Other Options Are Wrong:

Term 49 fits because the last difference from 37 to 49 is 12, matching the second 12 in the final pair. Term 37 is also correct because 25 to 37 is 12, the start of that pair. Term 25 fits as the second number after adding 8 twice. Term 9 fits the initial pair of plus 4 differences. None of these break the systematic pairwise pattern in the differences. Only 15 results in an irregular jump and destroys the pairwise structure of the series.

Common Pitfalls:

Students may try to fit a more complicated pattern involving squares or cubes, which is unnecessary in this case. Another common mistake is to focus on small parts of the series and ignore the overall pair structure in the differences. Some learners also assume that the incorrect term is likely at the end or beginning of the sequence without checking every transition. A disciplined approach is to compute all consecutive differences and look for neat groupings or repeating units; any violation typically indicates the wrong term.

Final Answer:

The term that violates the pattern of differences grouped in equal pairs is 15, so 15 is the wrong term in the series.