Complete the series 1, 4, 9, 16, ? & x20;

RRB Staff Nurse Delhi-2015

Reasoning

Medium

Complete the series 1, 4, 9, 16, ?

Appeared in: RRB Staff Nurse Delhi-2015

The series represents the squares of consecutive natural numbers starting from 1.
The first term is 1² = 1, the second is 2² = 4, the third is 3² = 9, and the fourth is 4² = 16.
Following this established pattern, the next term in the sequence must be the square of the next natural number, which is 5.
Calculating the next term: 5² = 5 × 5 = 25.

Option B: 36 is the square of 6 (6²). It represents the sixth term in the series, while the question asks for the fifth term.
Option C: 40 is not a perfect square of any integer and therefore does not fit the established pattern of the series.
Option D: 49 is the square of 7 (7²). It represents the seventh term in the series, which is two places after the required term.

Visual 1: Infographic: A visual chart showing the first ten natural numbers and their corresponding squares to illustrate the pattern (1²=1, 2²=4, 3²=9, etc.).

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.
Strong analytical and pattern-recognition skills help in interpreting patient data, recognizing trends in vital signs, and making sound clinical judgments.
For example, a nurse might notice a pattern of gradually increasing blood pressure readings over several hours, prompting a need for intervention.

How to Approach the Question

First, carefully examine the numbers in the series: 1, 4, 9, 16.
Look for a relationship or pattern between consecutive numbers. Calculate the difference between them (4-1=3, 9-4=5, 16-9=7). Notice the difference itself forms a pattern (3, 5, 7 - odd numbers).
Alternatively, check for common mathematical operations like squares, cubes, or multiplication/division by a constant factor.
Recognize that 1=1x1, 4=2x2, 9=3x3, and 16=4x4. This identifies the pattern as squares of consecutive natural numbers.
Apply the pattern to find the next term. Since the last given term is 4², the next term will be 5².
Calculate 5² (5 x 5 = 25) and select the matching option.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Delhi-2015

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