Completed the series-6, 8, 12, 20, 36?

Appeared in: HSSC Staff Nurse - 2015

Explanation

The question requires finding the next number in the sequence: 6, 8, 12, 20, 36.
The pattern is identified by calculating the difference between consecutive terms: 8-6=2, 12-8=4, 20-12=8, 36-20=16.
The differences themselves form a geometric progression (2, 4, 8, 16), where each subsequent difference is double the previous one.
Following this pattern, the next difference should be 16 × 2 = 32.
Adding this difference to the last term gives the next number in the series: 36 + 32 = 68.

Option A: This would imply a final difference of 30 (66-36), which does not fit the established pattern of doubling the difference (2, 4, 8, 16, ...).
Option B: This would imply a final difference of 22 (58-36), breaking the geometric progression of the differences.
Option C: This would imply a final difference of 27 (63-36). The number 27 is 3³, which does not follow the pattern of powers of 2 (2¹, 2², 2³, 2⁴).

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, number series problems are common in nursing entrance exams to assess logical reasoning and analytical skills.
These skills are crucial for nurses in clinical settings for tasks like calculating drug dosages, interpreting trends in vital signs, and making quick, logical decisions under pressure.
What if the series was arithmetic (e.g., 6, 8, 10, 12)? The pattern would be a constant addition (+2), and the next number would be 14. Recognizing different patterns is key to problem-solving.

How to Approach the Question

First, carefully examine the given series of numbers: 6, 8, 12, 20, 36.
Calculate the difference between each consecutive pair of numbers to look for a primary pattern.
The differences are: 8-6=2, 12-8=4, 20-12=8, 36-20=16.
Analyze the sequence of differences (2, 4, 8, 16) to find a secondary pattern. Notice that each number is double the previous one.
Extrapolate the pattern to find the next difference: 16 × 2 = 32.
Add this next difference to the last number in the original series to find the answer: 36 + 32 = 68.

Concept Tested & Keywords

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Practise the full HSSC Staff Nurse - 2015

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