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

Appeared in: DSSSB 14 August 2024

Explanation

The series progresses based on a consistent second-level difference between terms.
The first differences between consecutive terms are 21, 28, 35, and 42.
The second differences (the difference between the first differences) reveal a constant pattern of adding 7 (28-21=7, 35-28=7, etc.).
To find the next term, the next first difference is calculated by adding 7 to the last first difference (42 + 7 = 49).
Adding this new difference to the last term of the series gives the answer: 144 + 49 = 193.

Option A: This value does not follow the established mathematical pattern of the series.
Option B: This value does not fit the established pattern of a constant second difference of 7.
Option C: This would require the next difference to be 45 (144 + 45 = 189), which breaks the pattern of adding 7 to the previous difference.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series (Double Difference Pattern) as background academic context rather than a clinical decision trigger.
This type of logical reasoning question assesses analytical and problem-solving skills.
While not directly clinical, these skills are crucial for nurses in making quick, logical decisions, interpreting data patterns (like patient vital signs over time), and troubleshooting issues in a high-pressure environment.
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, examine the series to identify any obvious patterns (e.g., simple addition, subtraction, multiplication, squares).
Calculate the difference between consecutive terms. This is the first-level difference.
If the first-level differences are not constant or do not show a clear pattern, proceed to the next step.
Calculate the difference between the numbers in your new series of differences. This is the second-level difference.
Look for a constant value or a simple pattern in the second-level differences. In this case, the constant is 7.
Use this pattern to work backward. Add the constant second difference (7) to the last first difference (42) to get the next difference (49). Then, add this result to the last term of the original series (144) to find the answer (193).

Concept Tested & Keywords

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Practise the full DSSSB 14 August 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.