Find the number - 6, 9, 14, ..., 30

Appeared in: MNS 2015

Explanation

The core concept is identifying the mathematical pattern in a sequence of numbers.
The pattern in this series is the addition of consecutive odd numbers to each term.
The sequence of additions is +3, +5, +7, +9.
To find the missing term, the odd number 7 must be added to the preceding term, 14.
Calculation: 14 + 7 = 21.
To confirm, the next odd number (9) is added to 21, which correctly results in the final term, 30 (21 + 9 = 30).

Option A: Choosing 19 would mean adding 5 to 14. This is incorrect because the pattern requires adding the next consecutive odd number, which is 7, not repeating the previous addition of 5.
Option B: Choosing 20 would mean adding 6 to 14. This is incorrect because the established pattern involves adding only odd numbers, not even numbers.
Option D: Choosing 22 would mean adding 8 to 14. This is incorrect as it involves adding an even number, which violates the series' pattern of adding consecutive odd numbers.

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 is a foundational skill for nurses.
Nurses use pattern recognition daily to interpret trends in patient vital signs, lab results, and symptom progression to anticipate changes and intervene appropriately.
Strong problem-solving skills enable nurses to make sound clinical judgments quickly in high-pressure situations.

How to Approach the Question

First, analyze the given sequence: 6, 9, 14, ..., 30.
Calculate the difference between the initial consecutive terms to find a potential relationship. (9 - 6 = 3; 14 - 9 = 5).
Identify the pattern from these differences. The numbers being added (3, 5) are consecutive odd numbers.
Hypothesize the next step in the pattern. The next odd number after 5 is 7.
Apply this to find the missing term: 14 + 7 = 21.
Verify your answer by continuing the pattern to the next term. The odd number after 7 is 9. Adding this to your result (21 + 9) should equal the final term, 30. It does, confirming your logic.

Concept Tested & Keywords

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Practise the full MNS 2015

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