What should come in place of "?" in the given series? 18 39 67 102 144 ?

JIPMER Nursing Officer-2024

Reasoning

Hard

Appeared in: JIPMER Nursing Officer-2024

Explanation

The series follows a two-level pattern where the difference between consecutive terms is not constant.
The first level of differences is 21, 28, 35, 42.
The second level of differences (the difference of the differences) is a constant value of 7.
The next difference in the first level is calculated by adding 7 to the last difference (42 + 7 = 49).
The final term is found by adding this new difference to the last term of the series (144 + 49 = 193).

Option A: If the next term were 181, the difference from 144 would be 37. This would make the sequence of differences 21, 28, 35, 42, 37, which does not follow the established pattern of increasing by 7.
Option B: If the next term were 185, the difference from 144 would be 41. This disrupts the pattern where the difference increases by a constant 7.
Option C: If the next term were 189, the difference from 144 would be 45. The sequence of differences would be 21, 28, 35, 42, 45. The sub-difference would change from 7 to 3, breaking the pattern.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process: 1. Write down the series. 2. Calculate the first-level differences. 3. Calculate the second-level differences. 4. Identify the constant difference (7). 5. Project the next first-level difference. 6. Calculate the final term.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series Pattern Recognition as background academic context rather than a clinical decision trigger.
While not a clinical question, number series problems test logical reasoning and pattern recognition, which are crucial skills for nurses.
These skills are applied in clinical settings for tasks like interpreting trends in vital signs, calculating medication dosages over time, and recognizing patterns in patient symptoms.
What if the second difference was not constant? If the second difference also formed a pattern (e.g., an arithmetic or geometric progression), you would need to identify that third-level pattern to solve the series.

How to Approach the Question

First, look at the series and try to find a simple pattern like addition, subtraction, multiplication, or division by a constant number.
If no simple pattern is found, calculate the difference between consecutive terms (first-level difference).
Analyze the new sequence of differences. If it's constant, use it to find the next term. If it's not constant, calculate the difference of the differences (second-level difference).
Once you find a constant difference (in this case, at the second level), use it to work your way back up to find the next term in the original series.
Project the next number in the difference series, then add it to the last number of the original series to get the answer.

Concept Tested & Keywords

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