Find the next number in the series: 141, 137, 146, 130, 155, 119, ...

Introduction / Context:
This is a number series problem that involves observing changes between consecutive terms. The series 141, 137, 146, 130, 155, 119, ... may look irregular at first, but the differences between terms reveal a clear pattern. Spotting such patterns is a key skill in aptitude exams and helps strengthen numerical reasoning and pattern recognition.

Given Data / Assumptions:

• The series given is 141, 137, 146, 130, 155, 119, ...
• We must find the next term after 119.
• The pattern is likely encoded in the sequence of differences between consecutive terms.

Concept / Approach:
First compute the difference between each pair of consecutive terms. If these differences themselves follow a recognizable pattern, such as squares, alternating signs or constant changes, we can use that pattern to find the next difference and thus the next term. For more complex series, it is often helpful to look at the absolute values of differences separately from their signs.

Step-by-Step Solution:
Compute the differences: 137 − 141 = −4. 146 − 137 = +9. 130 − 146 = −16. 155 − 130 = +25. 119 − 155 = −36. So the sequence of differences is −4, +9, −16, +25, −36. Look at absolute values: 4, 9, 16, 25, 36. These are perfect squares: 2², 3², 4², 5², 6². The sign pattern alternates: negative, positive, negative, positive, negative. Following this pattern, the next square should be 7² = 49 with a positive sign. So the next difference should be +49. Therefore, the next term = 119 + 49 = 168.

Verification / Alternative check:
We can reconstruct the series using the identified rule: start at 141, subtract 2² to get 137, add 3² to get 146, subtract 4² to get 130, add 5² to get 155, subtract 6² to get 119, and then add 7² to reach 168. This sequence exactly matches the given terms and the next computed term, confirming that the pattern is consistent and correctly applied.

Why Other Options Are Wrong:

• 147, 162, 182 and 140: None of these correspond to adding 49 to 119, so they do not follow the discovered pattern of alternating plus and minus perfect squares.
• Any other value would break the neat progression of squared differences and alternating signs.

Common Pitfalls:
A frequent mistake is to search for a single arithmetic or geometric progression, which does not exist in the raw terms. Another is to check only the first few differences and give up when they do not appear constant. Instead, it is helpful to look at patterns in the differences themselves, such as squares, cubes or simple sequences with sign changes. Recognising that 4, 9, 16, 25 and 36 are consecutive squares is the key insight here.

Final Answer:
The next number in the series is 168.