Find the missing (?) in the series? 16, 28, 52, ?, 136 - NORCET 5 Prelims - Sept 2023 (Shift-2)

NORCET 5 Prelims - Sept 2023 (Shift-2)

Reasoning

Hard

Appeared in: NORCET 5 Prelims - Sept 2023 (Shift-2)

Explanation

The core concept is identifying a second-order arithmetic progression in the differences between the terms.
The difference between the first two terms (28 - 16) is 12.
The difference between the next two terms (52 - 28) is 24.
The pattern of differences is an arithmetic sequence: 12, 24, 36, 48 (each increasing by 12).
Adding the next difference (36) to the third term (52) gives the missing number: 52 + 36 = 88.
Verifying the final step, 88 + 48 = 136, confirms the pattern.

Option B: If the missing number were 96, the differences would be 12, 24, 44 (96-52), and 40 (136-96). This sequence of differences (12, 24, 44, 40) does not follow a logical or consistent mathematical pattern.
Option C: If the missing number were 86, the differences would be 12, 24, 34 (86-52), and 50 (136-86). This sequence of differences (12, 24, 34, 50) does not follow a consistent pattern.
Option D: If the missing number were 84, the differences would be 12, 24, 32 (84-52), and 52 (136-84). This sequence of differences (12, 24, 32, 52) lacks a clear, predictable mathematical rule.

Visual 1: Flowchart - A flowchart showing the step-by-step calculation. It would start with the series, branch to show the calculation of the first difference (12), the second difference (24), then show the calculation of the difference between differences (+12), and follow this logic to find the missing term (88) and verify the final term (136).

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, logical reasoning and pattern recognition are fundamental skills for nurses.
These skills are crucial for interpreting patient data, recognizing trends in vital signs, and identifying subtle changes in a patient's condition that may signal a developing problem.
For example, a nurse might notice a pattern of gradually increasing blood pressure readings over several hours, prompting a more thorough assessment and potential intervention.

How to Approach the Question

First, read the question and the number series carefully: 16, 28, 52, ?, 136.
Calculate the difference between the first and second terms (28 - 16 = 12).
Calculate the difference between the second and third terms (52 - 28 = 24).
Analyze the sequence of differences (12, 24, ...). Look for a pattern. In this case, the difference is increasing by 12 each time (an arithmetic progression).
Use this pattern to predict the next difference (24 + 12 = 36) and calculate the missing term (52 + 36 = 88).
Verify your answer by applying the pattern to the next step (next difference is 36 + 12 = 48; 88 + 48 = 136), ensuring it matches the final term in the series.

Concept Tested & Keywords

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