What number should replace the question mark in the following sequence?

12, 6, 6, 9, 18, ?

Appeared in: KPSC Staff Nurse - 2017

Explanation

The question requires identifying the pattern in a numerical sequence and finding the next number.
The pattern involves multiplying the current number by a factor that increases by 0.5 at each step.
The sequence of multipliers is 0.5, 1.0, 1.5, 2.0, and so on.
The first number (12) is multiplied by 0.5 to get 6.
The second number (6) is multiplied by 1.0 to get 6.
This pattern continues until the fifth number (18), which must be multiplied by the next factor in the series (2.5).

Option A: 36 would be the result if the multiplier was 2 (18 x 2), but the pattern requires the multiplier to be 2.5.
Option B: 30 does not fit the multiplicative pattern. To get 30 from 18, the multiplier would be approximately 1.67, which breaks the rule of the multiplier increasing by 0.5.
Option C: 48 does not follow the pattern. To get 48 from 18, the multiplier would be approximately 2.67, which is not 2.5.

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 changes in a patient's condition, interpret vital sign trends, and recognize adverse drug reactions.
Problem-solving skills are crucial for critical thinking in patient care, such as calculating drug dosages, adjusting IV drip rates, and troubleshooting equipment.

How to Approach the Question

First, examine the relationship between consecutive numbers in the sequence (12, 6, 6, 9, 18).
Check for simple arithmetic patterns: Is a constant number being added or subtracted? (e.g., 12-6 = 6, but 6-6 = 0. So, it's not a simple arithmetic series).
Check for simple geometric patterns: Is each number multiplied or divided by a constant factor? (e.g., 12/6 = 2, but 6/6 = 1. So, it's not a simple geometric series).
Look for a more complex pattern. Notice the relationship: 12 → 6 (halved), 6 → 6 (same), 6 → 9 (increased), 9 → 18 (doubled).
Test the hypothesis of a changing multiplier: 12 × 0.5 = 6. 6 × 1 = 6. 6 × 1.5 = 9. 9 × 2 = 18.
Confirm the pattern: The multiplier is increasing by 0.5 each time (0.5, 1.0, 1.5, 2.0).

Concept Tested & Keywords

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Practise the full KPSC Staff Nurse - 2017

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