Find the next number in this series ?

2,4,8,16....

Appeared in: Combined AIIMS - 2020 (Jodhpur, Bhopal, Patna, Raipur)

Explanation

The given series (2, 4, 8, 16) is a geometric progression.
In this series, each term is obtained by multiplying the preceding term by a constant number, known as the common ratio.
The common ratio here is 2 (since 4 ÷ 2 = 2, 8 ÷ 4 = 2, and so on).
To find the next term, the last term (16) is multiplied by the common ratio (2).
Calculation: 16 × 2 = 32.
Alternatively, the series represents powers of two: 2¹, 2², 2³, 2⁴. The next term is 2⁵, which equals 32.

Option A: This value does not follow the established pattern of multiplying the previous term by 2.
Option B: This is the fourth term of the series, not the next (fifth) term.
Option C: This value does not fit the geometric progression of multiplying by 2.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Geometric Progression as background academic context rather than a clinical decision trigger.
This question assesses logical reasoning and pattern recognition, foundational skills for a nurse.
While not a direct clinical task, these skills are crucial for interpreting trends in patient data, like vital signs or lab results, to anticipate changes in a patient's condition.
What if the series was 2, 4, 6, 8? This would be an arithmetic progression with a common difference of 2, and the next number would be 10. Recognizing the type of pattern is key.

How to Approach the Question

Step 1: Analyze the sequence of numbers provided: 2, 4, 8, 16.
Step 2: Identify the mathematical relationship between consecutive numbers. Ask yourself if they are related by addition, subtraction, multiplication, or division.
Step 3: Observe that each number is twice the previous number (4 = 2 × 2; 8 = 4 × 2; 16 = 8 × 2).
Step 4: Conclude that the series is a geometric progression with a common ratio of 2.
Step 5: Apply this pattern to the last number in the series to find the next term: 16 × 2.
Step 6: Calculate the result (32) and select the matching option.

Concept Tested & Keywords

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Practise the full Combined AIIMS - 2020 (Jodhpur, Bhopal, Patna, Raipur)

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