Find the next number in this series ?

2,4,8,16..?

Appeared in: NORCET 3 - 2022 (Shift-2)

Explanation

The series presented is a classic example of a Geometric Progression (GP).
In this series, each subsequent number is obtained by multiplying the previous number by a constant factor, which is 2 in this case (this is called the common ratio).
The pattern is: 2, (2 × 2) = 4, (4 × 2) = 8, (8 × 2) = 16.
To find the next term, you apply the same rule to the last known term: 16 × 2 = 32.
Alternatively, the series can be viewed as powers of 2: 2¹, 2², 2³, 2⁴, so the next term is 2⁵, which equals 32.

Option A: The number 40 does not fit the established pattern of doubling the previous number. Moving from 16 to 40 would require multiplying by 2.5, which breaks the consistent 'multiply by 2' rule.
Option B: The number 16 is the last term given in the question, not the next term in the sequence. The question asks to find the number that comes after 16.
Option C: The number 30 does not follow the geometric progression. This might be a guess by someone trying to apply an arithmetic pattern incorrectly. The difference between terms is not constant (+2, +4, +8), so an arithmetic rule does not apply.

Visual 1: Flowchart. A simple diagram illustrating the progression: 2 → (multiplied by 2) → 4 → (multiplied by 2) → 8 → (multiplied by 2) → 16 → (multiplied by 2) → 32. This visually reinforces the pattern.

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 logical reasoning and pattern recognition, which are fundamental cognitive skills for problem-solving in any professional field.
In nursing, similar pattern recognition is crucial for interpreting clinical data. For example, identifying a consistent trend in a patient's vital signs (like a steadily increasing heart rate or a progressively dropping blood pressure) allows for timely intervention.
This skill helps in anticipating patient needs, recognizing the early signs of deterioration, and evaluating the effectiveness of treatments over time.

How to Approach the Question

First, examine the relationship between the first few numbers in the series to identify a pattern.
Calculate the difference between consecutive numbers: 4 - 2 = 2; 8 - 4 = 4; 16 - 8 = 8. Since the difference is not constant, it's not an arithmetic progression.
Calculate the ratio between consecutive numbers: 4 / 2 = 2; 8 / 4 = 2; 16 / 8 = 2. Since the ratio is constant, it's a geometric progression with a common ratio of 2.
Apply the identified rule to the last term of the series to find the next term.
Multiply the last term, 16, by the common ratio, 2. The result is 16 × 2 = 32.
Compare your result with the given options and select the matching one.

Concept Tested & Keywords

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Practise the full NORCET 3 - 2022 (Shift-2)

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