What should come in place of '?' in the given series? 12 31 54 81 112 ?

Appeared in: DSSSB October 2024

Explanation

The series follows a pattern where the difference between consecutive numbers increases by a constant amount.
The first-order differences are 19, 23, 27, and 31.
The second-order difference (the difference between the first-order differences) is a constant value of 4 (e.g., 23 - 19 = 4).
To find the next term, the next first-order difference must be the previous one plus the constant second-order difference: 31 + 4 = 35.
Adding this new difference to the last term of the series gives the correct answer: 112 + 35 = 147.

Option A: This option results from adding 41 (153 - 112) to the last term, which does not follow the established pattern of adding 4 to the previous difference.
Option B: This option results from adding 27 (139 - 112) to the last term. This incorrectly repeats a previous difference (81 - 54 = 27) instead of progressing the pattern.
Option C: This option results from adding 19 (131 - 112) to the last term. This incorrectly repeats the very first difference of the series, breaking the clear progression.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series with a constant second-order difference as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, the logical reasoning skills tested are crucial for nursing practice.
Nurses use pattern recognition daily to analyze trends in patient vital signs, lab results, and symptoms to anticipate changes in a patient's condition.
Strong analytical skills help in prioritizing care, making sound clinical judgments, and solving problems effectively in a high-pressure environment.

How to Approach the Question

First, examine the series to identify any simple arithmetic pattern (e.g., constant addition, multiplication).
If a simple pattern isn't obvious, calculate the differences between consecutive terms to create a new series (the 'first-order differences').
Analyze this new series of differences for a pattern. In this case, the differences are 19, 23, 27, 31.
If the pattern is still not clear, repeat the process: calculate the differences of the new series (the 'second-order differences'). Here, 23-19=4, 27-23=4, etc.
Once you find a constant difference (in this case, 4), use it to work your way back up. Predict the next first-order difference (31 + 4 = 35).
Finally, use that predicted difference to find the next term in the original series (112 + 35 = 147).

Concept Tested & Keywords

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Practise the full DSSSB October 2024

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