Find the missing term in the given series : 14, 27, 52, 101, 198, ?

Appeared in: Haryana CHO -2023

Explanation

The series follows the pattern: Next Term = (Previous Term × 2) - n, where 'n' is a sequential number starting from 1 and increasing by one for each subsequent term.
First term calculation: (14 × 2) - 1 = 27.
Second term calculation: (27 × 2) - 2 = 52.
Third term calculation: (52 × 2) - 3 = 101.
Fourth term calculation: (101 × 2) - 4 = 198.
Following this established pattern, the missing term is calculated from the last known term (198): (198 × 2) - 5 = 396 - 5 = 391.

Option A: This is incorrect. It may result from a miscalculation, such as subtracting a larger number (e.g., 15) or using an incorrect multiplier in the final step.
Option B: This is incorrect. This value might be obtained if one incorrectly subtracts 1 instead of 5 in the final step (396 - 1 = 395), failing to follow the sequential increase of the subtracted number.
Option D: This is incorrect. This value might be obtained if one incorrectly subtracts 2 instead of 5 in the final step (396 - 2 = 394), failing to follow the sequential increase of the subtracted number.

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, this type of logical reasoning is a foundational skill for nurses.
Nurses use pattern recognition daily to identify trends in patient vital signs, lab results, and symptom progression, which is crucial for early detection of complications.
Strong problem-solving skills help in prioritizing care, troubleshooting equipment, and making sound clinical judgments under pressure.

How to Approach the Question

First, carefully examine the relationship between consecutive numbers in the series.
Look for common patterns like addition, subtraction, multiplication, division, squares, or cubes.
In this case, notice that each number is roughly double the previous one. This suggests a pattern involving multiplication by 2.
Calculate the difference after doubling: 14×2=28 (actual is 27), 27×2=54 (actual is 52), 52×2=104 (actual is 101). Observe that the amount subtracted increases sequentially (1, 2, 3...).
Formulate the rule: Next Term = (Previous Term × 2) - n, where n starts at 1 and increases by 1 for each step.
Apply this rule to the last given term (198) to find the missing number.

Concept Tested & Keywords

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Practise the full Haryana CHO -2023

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