Select the suitable alternative to complete the series. 0, 7, 26, ?, 124, 215

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The series follows a consistent mathematical pattern where each term is derived from the cube of its position number (n) minus one.
The general formula for any term in the series is Tₙ = n³ - 1.
For the missing fourth term, n is equal to 4.
The calculation for the fourth term is 4³ - 1, which equals 64 - 1 = 63.

Option A: The number 80 does not fit the established pattern of n³ - 1. For n=4, the result is 63. 80 would correspond to approximately 4.3³ - 1, breaking the integer sequence.
Option B: The number 47 does not follow the n³ - 1 rule. It is 16 less than the correct value of 63.
Option C: The number 51 is incorrect as it does not conform to the n³ - 1 pattern. It is 12 less than the correct value of 63.

Visual 1: Infographic: A visual chart showing the sequence of natural numbers (n=1 to 6), the calculation of their cubes (n³), and the final step of subtracting 1 to get the terms of the series, highlighting the missing term.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number series based on a cubic pattern as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, strong numerical reasoning is a fundamental skill for nurses.
Nurses constantly use mathematical skills for critical tasks like calculating medication dosages, setting IV infusion rates, and interpreting patient data, where accuracy is vital for patient safety.
A mistake in calculation can lead to significant adverse events, making numerical proficiency a core competency in nursing.

How to Approach the Question

First, carefully observe the given numbers in the series: 0, 7, 26, ?, 124, 215.
Try to find a simple arithmetic pattern (adding or subtracting a constant number). The differences are 7, 19, etc., so this is not an arithmetic series.
Check for a geometric pattern (multiplying or dividing by a constant number). This is also not the case.
Look for patterns involving squares (n²) or cubes (n³) of the term's position (n=1, 2, 3...).
Notice that the terms are very close to perfect cubes: 1³=1, 2³=8, 3³=27, 5³=125, 6³=216.
Test the hypothesis that each term is the cube of its position minus 1 (n³ - 1).

Concept Tested & Keywords

Q233WqTIDbaOhV6ZOGptuK

Practise the full ESIC Nursing Officer 2016 (Shift -2)

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