दी गई श्रेणी में अगली संख्या क्या होगी?

2,6, 18, 54,?

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

The series provided is 2, 6, 18, 54, ...
This is a Geometric Progression (GP) where each term is found by multiplying the previous term by a constant number (the common ratio).
To find the common ratio, divide any term by its preceding term: 6 ÷ 2 = 3; 18 ÷ 6 = 3.
The common ratio (r) is 3.
To find the next term in the series, multiply the last term (54) by the common ratio (3).
Calculation: 54 × 3 = 162.

Option A: The number 108 would be the result of multiplying the last term (54) by 2. This breaks the established pattern of multiplying by 3.
Option B: The number 152 does not follow any simple arithmetic or geometric relationship with the previous term, 54. For instance, 152 - 54 = 98, and 152 / 54 is not an integer.
Option D: The number 181 does not fit the geometric progression. It is likely included as a distractor to confuse test-takers.

Visual 1: Flowchart - A flowchart illustrating the geometric progression: Start with 2 → (Multiply by 3) → Get 6 → (Multiply by 3) → Get 18 → (Multiply by 3) → Get 54 → (Multiply by 3) → Get 162.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Identifying the pattern in a geometric progression number series as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and pattern recognition, a fundamental skill for problem-solving in any field, including nursing.
While not directly clinical, nurses use similar sequential thinking to track patient vital signs over time, noticing trends (e.g., a steadily increasing heart rate) and predicting potential changes or deterioration.
What if? - If the series was an arithmetic progression like 2, 6, 10, 14, the pattern would be adding 4 each time, and the next number would be 18.

How to Approach the Question

First, examine the relationship between the first few numbers in the series (2, 6, 18) to identify a pattern.
Check for a common difference (arithmetic progression): 6 - 2 = 4, but 18 - 6 = 12. The difference is not constant, so it's not an arithmetic series.
Check for a common ratio (geometric progression): 6 ÷ 2 = 3, and 18 ÷ 6 = 3. The ratio is constant.
Confirm the pattern with the next number in the series: 18 × 3 = 54. The pattern holds true.
Apply the identified rule (multiply by 3) to the last given term (54) to find the missing number.
Calculate the final answer: 54 × 3 = 162.

Concept Tested & Keywords

Concept Tested: Identifying the pattern in a geometric progression number series.
Stem keywords: number series, next number, geometric progression
Lead-in keywords: what will be the next number

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