Identify the next number in the following series: 3, 6, 9, 10, 9, 18, 17, 34, ?

Appeared in: AIIMS CRE 2025

Explanation

The series follows a clear, alternating pattern in its latter half: multiply by 2, then subtract 1.
Starting from the number 9, the sequence is: (9 x 2) = 18; (18 - 1) = 17; (17 x 2) = 34.
Applying the next step in the pattern, which is subtracting 1, gives the answer.
Calculation: 34 - 1 = 33.

Option A: 34 is the last given number in the series. The question asks for the next number, which requires applying the next step of the pattern.
Option C: 35 would result from adding 1 to 34. The established pattern is (x 2, - 1), not (+ 1).
Option D: 36 would result from adding 2 to 34. This does not fit the (x 2, - 1) pattern identified in the series.

Visual 1: Flowchart: A flowchart illustrating the alternating pattern (x 2) and (- 1) applied to the series 9, 18, 17, 34, to arrive at 33. This would visually reinforce the logic.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and pattern recognition, which are fundamental cognitive skills.
While not directly clinical, these skills are crucial for nurses in problem-solving, interpreting changing patient data, and making quick, logical decisions in complex situations.
What if the pattern was (+3, +1)? The series would look very different (e.g., 3, 6, 7, 10...). The ability to correctly identify the underlying rule is the key skill being assessed.

How to Approach the Question

First, examine the series to identify the relationship between consecutive numbers.
Look for simple arithmetic operations: addition, subtraction, multiplication, or division.
If a simple pattern doesn't fit the entire series, look for alternating patterns, where two or more different operations are applied in sequence.
In this series (3, 6, 9, 10, 9, 18, 17, 34), notice that the numbers sometimes increase and sometimes decrease, suggesting an alternating pattern.
Test the hypothesis of an alternating pattern (x 2, - 1) on the latter, more consistent part of the series (9, 18, 17, 34).
Once the pattern is confirmed, apply the next logical step to the last number (34) to find the answer.

Concept Tested & Keywords

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Practise the full AIIMS CRE 2025

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