Identify the next number in the sequence.

1, 2, 4, 7, 11, _____

Appeared in: NORCET 1 - 2020

Explanation

The sequence progresses by adding consecutive integers to each subsequent term.
The difference between the first and second term (2-1) is 1.
The difference between the second and third term (4-2) is 2.
This pattern continues with differences of 3, and 4. Therefore, the next difference must be 5.
Adding 5 to the last known term (11) gives the next number in the sequence: 11 + 5 = 16.

Option A: Choosing 14 implies the next difference is 3 (11 + 3 = 14), which breaks the pattern of consecutively increasing differences (1, 2, 3, 4, ...).
Option C: Choosing 12 implies the next difference is 1 (11 + 1 = 12). This contradicts the established pattern of the difference increasing by 1 each time.
Option D: Choosing 10 would mean the sequence is decreasing, which contradicts the clear increasing trend of all previous terms.

Visual 1: Infographic - A flowchart showing the sequence 1, 2, 4, 7, 11 with arrows indicating '+1', '+2', '+3', '+4' between the numbers, and a final '+5' leading to 16.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning: Number Series as background academic context rather than a clinical decision trigger.
Logical reasoning questions are a standard component of nursing entrance exams, testing a candidate's problem-solving and analytical skills.
These skills are crucial in clinical settings for tasks like calculating drug dosages, interpreting patient data trends, and making quick, logical decisions under pressure.
What if the sequence was 1, 2, 4, 8, 16? The pattern would be multiplication by 2 (a geometric progression), and the next number would be 32. Recognizing different types of patterns is key.

How to Approach the Question

First, examine the relationship between the first few numbers to identify a potential pattern. Look for addition, subtraction, multiplication, or division.
Calculate the difference between each consecutive pair of numbers: (2-1=1), (4-2=2), (7-4=3), (11-7=4).
Analyze the sequence of differences you just calculated: 1, 2, 3, 4. This is a simple arithmetic progression.
Determine the next number in the sequence of differences, which is clearly 5.
Apply this next difference to the last number in the original sequence to find the answer: 11 + 5 = 16.
Finally, check if your calculated answer is among the given options.

Concept Tested & Keywords

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Practise the full NORCET 1 - 2020

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