Identify the next number in the sequence: 1, 2, 4, 7, 11, _____

Appeared in: KPSC Staff Nurse - 2015

Explanation

The sequence follows a pattern where the difference between consecutive numbers increases by 1 each time.
The difference between the first two numbers (1 and 2) is 1.
The difference between the next pair (2 and 4) is 2.
This continues with a difference of 3 (4 and 7), and then 4 (7 and 11).
Therefore, the next difference in the series must be 5.
Adding 5 to the last number in the sequence, 11, gives the next term: 11 + 5 = 16.

Option A: Choosing 14 would imply adding 3 to 11. This breaks the established pattern of the difference increasing by one each time (1, 2, 3, 4, ...). The previous difference was 4, so the next should be 5, not 3.
Option C: Choosing 12 would imply adding 1 to 11. This contradicts the pattern of consistently increasing differences.
Option D: Choosing 10 is incorrect because the sequence is clearly increasing. Each number is greater than the one before it. 10 is less than 11.

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.
Nurses use pattern recognition daily to interpret vital sign trends, lab value changes, and symptom progression, allowing for early identification of patient deterioration or improvement.
What if the sequence was 1, 2, 4, 8, 16? The pattern would be multiplication by 2 (doubling), and the next number would be 32. This demonstrates that the first step is always to find the relationship between the numbers.

How to Approach the Question

First, look at the sequence and determine if it's increasing, decreasing, or alternating.
Calculate the difference between the first two numbers (2 - 1 = 1).
Calculate the difference between the next pairs of numbers (4 - 2 = 2; 7 - 4 = 3; 11 - 7 = 4).
Analyze the set of differences you've found (1, 2, 3, 4). Identify the pattern in this new sequence.
The pattern is a simple progression of consecutive integers. Predict the next difference will be 5.
Apply this difference to the last number of the original sequence (11 + 5) to find the answer.

Concept Tested & Keywords

QH-rC1lXhJLxpNUS8aCF0L

Practise the full KPSC Staff Nurse - 2015

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