Identify the missing number in the following sequence: 1, 9, 25, 49, __, 121

Appeared in: SGPGI Nursing Officer-2023

Explanation

Option A: 64 is the square of 8 (8²). The pattern requires the square of an odd number, not an even number.
Option B: 72 is not a perfect square and does not fit the pattern of squares of consecutive odd numbers.
Option D: 100 is the square of 10 (10²). The pattern is based on squares of odd numbers, and 10 is an even number.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series and Pattern Recognition as background academic context rather than a clinical decision trigger.
This question tests numerical reasoning, a key component of the General Intelligence and Aptitude sections of many nursing entrance and recruitment exams.
Being able to quickly identify mathematical patterns (like squares, cubes, or arithmetic progressions) is a crucial skill for scoring well and managing time effectively in these competitive exams.
What if the sequence was 4, 16, 36, 64, __, 144? The pattern would be squares of consecutive even numbers (2², 4², 6², 8², 10², 12²), and the missing number would be 100.

How to Approach the Question

First, carefully examine the numbers in the sequence: 1, 9, 25, 49, __, 121.
Try to identify a common mathematical property. Notice that all the given numbers are perfect squares.
Determine the square root of each number: √1=1, √9=3, √25=5, √49=7, √121=11.
Analyze the resulting sequence of roots: 1, 3, 5, 7, __, 11.
Recognize that this is a simple sequence of consecutive odd numbers.
Identify the missing odd number between 7 and 11, which is 9.

Concept Tested & Keywords

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Practise the full SGPGI Nursing Officer-2023

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