Find the next number in the series.& x20; 3, 4, 7, 16, 43, ?

RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

Reasoning

Hard

Find the next number in the series.

3, 4, 7, 16, 43, ?

Appeared in: RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

The pattern is found by calculating the difference between consecutive terms: 4-3=1, 7-4=3, 16-7=9, 43-16=27.
These differences (1, 3, 9, 27) are consecutive powers of 3 (3⁰, 3¹, 3², 3³).
To find the next number, the next power of 3 (3⁴ = 81) must be added to the last term of the series.
Calculation: 43 + 81 = 124.

Option A: This would mean the difference is 98 - 43 = 55, which does not fit the pattern of powers of 3 (1, 3, 9, 27, ...).
Option B: This implies a difference of 112 - 43 = 69. This value does not follow the established geometric progression of differences (1, 3, 9, 27).
Option C: This would require adding 86 - 43 = 43. This number does not fit the sequence of differences (1, 3, 9, 27), which are powers of 3.

Visual 1: Flowchart - A flowchart showing the steps: Start with the series -> Calculate differences -> Identify the pattern (powers of 3) -> Calculate the next difference (3⁴=81) -> Add to the last term (43+81) -> Arrive at the final answer (124).

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, number series problems test logical and analytical reasoning, which are crucial skills for nurses.
Nurses use pattern recognition daily for tasks like interpreting vital sign trends, titrating medication drips based on patient response, and identifying subtle changes in a patient's condition.
What if the series was 3, 4, 6, 9, 13? The pattern would be adding consecutive integers (+1, +2, +3, +4), and the next number would be 13 + 5 = 18. This highlights the importance of correctly identifying the underlying rule.

How to Approach the Question

First, write down the series and look for an obvious pattern (e.g., simple addition, subtraction, or multiplication).
If the pattern isn't immediately clear, calculate the difference between each consecutive number.
Analyze the new series of differences. Look for a pattern here. In this case, the differences are 1, 3, 9, 27.
Recognize that this sequence of differences is a geometric progression (each number is multiplied by 3) or, equivalently, powers of 3 (3⁰, 3¹, 3², 3³).
Determine the next term in the difference sequence (3⁴ = 81).
Add this next difference to the last term of the original series to find the missing number (43 + 81 = 124).

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

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