Find the next number in the series. 78, 65, 82, 69, 86, ?

Appeared in: NORCET 2 -2021 (Shift-2)

Explanation

The sequence follows a dual pattern, which can be identified in two primary ways.
Method 1 (Alternating Operations): The series alternates between subtracting 13 and adding 17. The last operation was adding 17 (69 + 17 = 86), so the next operation is subtracting 13. 86 - 13 = 73.
Method 2 (Interleaved Series): The sequence consists of two separate series. The first is 78, 82, 86... (increasing by 4). The second is 65, 69, ?... (also increasing by 4). The next term in the second series is 69 + 4 = 73.

Option B: This number does not fit the established pattern of either subtracting 13 or adding 4 to the relevant preceding term.
Option C: This number does not follow the alternating pattern. The next logical step is a subtraction, not an addition, and the value is incorrect for either of the interleaved series.
Option D: This number does not fit the pattern. The next term should be 86 - 13 = 73, not 79.

Visual 1: Flowchart - A diagram illustrating the 'Alternating Operations' method, showing '78 -> (-13) -> 65 -> (+17) -> 82 -> (-13) -> 69 -> (+17) -> 86 -> (-13) -> 73'.
Visual 2: Diagram - A visual separating the sequence into two interleaved series, one in blue (78, 82, 86) and one in red (65, 69, 73), with arrows showing the '+4' progression in each.

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.
This question tests logical reasoning and pattern recognition, which are foundational skills for problem-solving in any field, including nursing.
While not a clinical question, the ability to quickly identify patterns is analogous to recognizing trends in a patient's vital signs or lab results, which is a critical nursing skill.
What if the series was 78, 65, 52, 39...? In this case, the pattern is a simple subtraction of 13 each time. The next number would be 39 - 13 = 26. This highlights the importance of correctly identifying the specific pattern at play.

How to Approach the Question

First, read the series carefully: 78, 65, 82, 69, 86, ?.
Calculate the difference between consecutive terms: -13, +17, -13, +17. This reveals a clear alternating pattern.
Apply the next logical operation in the pattern (-13) to the last number (86) to find the answer: 86 - 13 = 73.
Alternatively, check for an interleaved pattern. Separate the numbers in odd positions (78, 82, 86) and even positions (65, 69, ?).
Identify the pattern in each sub-series. Both are increasing by 4.
Calculate the next term for the series in the even positions: 69 + 4 = 73.

Concept Tested & Keywords

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Practise the full NORCET 2 -2021 (Shift-2)

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