Identify the missing number in the following sequence: 1, 8, 27, __, 125, 216?

Appeared in: SGPGI Nursing Officer-2023

Explanation

The sequence follows a pattern of perfect cubes of natural numbers, represented by the formula n³.
The first term is 1³ = 1, the second is 2³ = 8, and the third is 3³ = 27.
The missing term is the fourth number in the sequence, which is calculated as 4³ = 4 × 4 × 4 = 64.
The subsequent terms, 5³ = 125 and 6³ = 216, confirm this established pattern.

Option A: 16 is the square of 4 (4²), not the cube of 4. The series pattern is based on cubes (n³).
Option C: 36 is the square of 6 (6²). The pattern requires the cube of 4, not the square of 6.
Option D: 49 is the square of 7 (7²). This does not fit the sequence of cubes.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number series and patterns as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, strong numeracy skills are critical for nurses in daily practice.
Nurses perform calculations for drug dosages, IV drip rates, and fluid balance monitoring, all of which require mathematical accuracy.
Understanding mathematical patterns helps in quickly verifying calculations and spotting potential errors, which is a key patient safety measure.

How to Approach the Question

First, examine the numbers in the sequence: 1, 8, 27, __, 125, 216.
Observe the relationship between the numbers. They are increasing rapidly, which suggests a pattern involving multiplication or exponents.
Test for common mathematical sequences. Check if they are perfect squares (1, 4, 9, 16...) or perfect cubes (1, 8, 27, 64...).
Recognize that 1 = 1³, 8 = 2³, and 27 = 3³. This confirms the pattern is the cube of consecutive natural numbers (n³).
Identify the position of the missing number. It is the fourth term in the sequence.
Apply the pattern to find the missing term by calculating 4³, which equals 64.

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.