Complete the series------ 4, 16, 5, 25, 6,....?

Appeared in: AIIMS Manglagiri NO - 2019

Explanation

The series follows a pattern of a number followed by its square.
The sequence is structured in pairs: (n, n²).
The first pair is (4, 4²), which is (4, 16).
The second pair is (5, 5²), which is (5, 25).
Following this logic, the third pair starts with 6, so the next term must be 6², which is 36.

Option A: The value 15 does not fit the established pattern. It is not the square of 6.
Option B: The value 7 would continue the sequence of the first number in each pair (4, 5, 6, ...), but it ignores the immediate pattern of a number being followed by its square.
Option D: The value 49 is the square of 7 (7²), not the square of 6. It would be the correct answer if the preceding number in the pair was 7.

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 skills are crucial for nurses in prioritizing tasks, interpreting data, and making sound clinical judgments under pressure.
Pattern recognition helps in identifying trends in a patient's vital signs or symptoms, allowing for early detection of deterioration or improvement.
What if the series was 4, 8, 5, 10, 6, ...? The pattern would change to (n, 2n). The answer would then be 12 (6 x 2), demonstrating the importance of correctly identifying the underlying rule.

How to Approach the Question

First, carefully observe the numbers in the series to identify any immediate relationship between adjacent numbers.
Look for common mathematical operations: addition, subtraction, multiplication, division, squares, cubes, or a combination of these.
In this series, notice that 16 is the square of 4, and 25 is the square of 5. This suggests a repeating pattern.
Group the numbers into pairs: (4, 16), (5, 25), (6, ...).
Confirm the pattern: The second number in each pair is the square of the first.
Apply the pattern to the last number, 6, to find the missing term: 6² = 36.

Concept Tested & Keywords

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Practise the full AIIMS Manglagiri NO - 2019

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