Find the next number in the series.

9, 13, 21, 37, 69, ?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

Explanation

The core of this question is to identify the relationship between consecutive numbers in the given series.
First, calculate the difference between each pair of numbers: 13-9=4, 21-13=8, 37-21=16, 69-37=32.
Observe that the differences (4, 8, 16, 32) form a geometric progression, where each subsequent difference is double the previous one.
To find the next number, continue the pattern: the next difference will be 32 × 2 = 64.
Add this difference to the last number in the series: 69 + 64 = 133.

Option A: Choosing 127 would mean the difference is 127 - 69 = 58. This value does not fit the established pattern of doubling the previous difference (which was 32).
Option B: Selecting 131 implies a difference of 131 - 69 = 62. This breaks the consistent doubling pattern (32 x 2 = 64, not 62).
Option C: If the answer were 129, the difference would be 129 - 69 = 60. This does not align with the pattern, which requires the next difference to be 64.

Visual 1: Flowchart - A flowchart could visually break down the process: Start with the series -> Calculate differences between terms -> Identify the 'doubling' pattern in the differences -> Calculate the next difference (32 * 2 = 64) -> Add it to the last term (69 + 64) -> Arrive at the final answer (133).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series Pattern Recognition as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning is a fundamental skill for nurses.
Nurses use pattern recognition daily to identify trends in patient vital signs, symptom progression, or lab results, which is crucial for early detection of patient deterioration.
Problem-solving skills are essential for troubleshooting equipment, managing complex patient care scenarios, and making sound clinical judgments under pressure.

How to Approach the Question

First, read the series carefully: 9, 13, 21, 37, 69.
Calculate the difference between consecutive numbers to look for a simple arithmetic pattern. (13-9=4, 21-13=8, etc.)
Analyze the differences themselves (4, 8, 16, 32). Look for a relationship between these numbers.
Recognize that the differences are doubling each time (a geometric progression with a common ratio of 2).
Apply this rule to find the next logical difference in the sequence (32 x 2 = 64).
Add this calculated difference to the last number of the original series to find the answer (69 + 64 = 133).

Concept Tested & Keywords

QwhSbAlGeS5c6Hu6vsdlml

Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

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