Find the next number in the series?

3, 7, 16, 35, 74, ?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-2)

Explanation

The series follows the pattern where the next number is calculated as (Previous Number × 2) + n.
The value of 'n' starts at 1 and increments by 1 for each subsequent term in the series.
The first term is 3. The second is (3 × 2) + 1 = 7.
The third is (7 × 2) + 2 = 16.
The fourth is (16 × 2) + 3 = 35.
The fifth is (35 × 2) + 4 = 74.

Option A: This number does not follow the established pattern. To get 187 from 74, the calculation would be (74 x 2) + 39. The number to be added should be 5, not 39.
Option B: This value is too high and does not fit the sequence logic. To get 223, the calculation would be (74 x 2) + 75. The pattern requires adding 5.
Option D: This number does not fit the pattern. It is the result of (74 x 2) - 1 = 147. The established pattern involves adding an increasing positive integer, not subtracting.

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 foundational skill for nurses.
It enhances problem-solving abilities, which are crucial for analyzing patient data, identifying patterns in symptoms, and making sound clinical judgments.
What if the pattern was (x * 3) - 2? The series would be 3, 7, 19, 55... This demonstrates how quickly a small change in the underlying rule alters the entire sequence, highlighting the need for careful analysis.

How to Approach the Question

First, examine the relationship between consecutive numbers. Calculate the difference between them: 7-3=4, 16-7=9, 35-16=19, 74-35=39. The differences are not constant, so it's not a simple arithmetic series.
Next, check for a multiplication or division pattern. 7/3, 16/7, etc., are not constant ratios.
Look for a combination of arithmetic and geometric operations. Test a pattern like (previous number × k) + c.
Test with k=2: (3 × 2) = 6. To get 7, you add 1. Let's see if this holds.
Test the next term: (7 × 2) = 14. To get 16, you add 2.
A pattern emerges: (previous number × 2) + n, where n starts at 1 and increases by 1 each time.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-2)

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