Sequence: 2, 4, 8, 16. What is the next number?

Appeared in: RML PRE 2025

Explanation

The sequence 2, 4, 8, 16 is a classic example of a geometric progression.
In this pattern, each subsequent number is obtained by multiplying the previous number by a fixed value, known as the common ratio.
Observing the sequence, 4 is 2 × 2, 8 is 4 × 2, and 16 is 8 × 2. The common ratio is 2.
To find the next term after 16, you apply the same rule: 16 × 2 = 32.

Option B: This option incorrectly assumes an additive pattern. While 16 + 8 = 24, adding 8 is not the rule governing the sequence; the rule is to multiply by 2.
Option C: This option incorrectly assumes a simple additive pattern of +4. This does not align with the doubling relationship seen between all other terms in the sequence.
Option D: This number does not fit any simple mathematical pattern (neither arithmetic nor geometric) based on the term 16. It is an arbitrary distractor.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Identifying patterns in a number sequence (Geometric Progression) as background academic context rather than a clinical decision trigger.
Logical reasoning and pattern recognition are foundational skills for nurses, essential for interpreting data, identifying trends in patient vitals, and making quick, accurate decisions.
While this is a math problem, the underlying skill of identifying a progression is similar to recognizing the worsening or improvement of a patient's condition over time based on clinical data (e.g., a steady increase in temperature or decrease in oxygen saturation).
What if? - If the sequence was reversed (16, 8, 4, 2), the pattern would be dividing by 2 (or multiplying by 0.5). The next number would be 1. This is analogous to recognizing a trend of de-escalation in a patient's symptoms or lab values, indicating improvement.

How to Approach the Question

First, analyze the relationship between the first two numbers (2 and 4). The relationship could be addition (+2) or multiplication (×2).
Next, check if this relationship holds for the next pair of numbers (4 and 8). Adding 2 (4+2) gives 6, which is incorrect. Multiplying by 2 (4×2) gives 8. This confirms the pattern is multiplication.
Verify the pattern with the final given pair (8 and 16). Indeed, 8 × 2 = 16. The pattern is confirmed as a geometric progression with a common ratio of 2.
Apply this established rule to the last number in the sequence (16) to find the next term: 16 × 2 = 32.
Finally, select the option that matches your calculated result.

Concept Tested & Keywords

Concept Tested: Identifying patterns in a number sequence (Geometric Progression).
Stem keywords: Sequence, 2, 4, 8, 16, next number
Lead-in keywords: What is

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Practise the full RML PRE 2025

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