Find the missing number in the following number series. -15, -7, ___, 14, 26

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

The core of solving this problem is to find the pattern in the differences between consecutive terms.
The series is -15, -7, ___, 14, 26. The first difference is -7 - (-15) = 8, and the last difference is 26 - 14 = 12.
This suggests the differences are increasing from 8 to 12.
If we insert 3 as the missing number, the series becomes -15, -7, 3, 14, 26.
The differences between terms become 8, 10, 11, and 12.
This sequence of differences (8, 10, 11, 12) is a logical progression, as it's a sequence of increasing integers, making 3 the correct missing number.

Option A: If 1 is the missing number, the differences are 8, 8, 13, 12. This sequence is erratic and does not follow a discernible mathematical pattern.
Option B: If 2 is the missing number, the differences are 8, 9, 12, 12. The sudden jump from 9 to 12 and the subsequent repetition of 12 makes the pattern less logical than a simple increasing sequence.
Option C: If 0 is the missing number, the differences are 8, 7, 14, 12. The sequence of differences is not monotonic (it decreases then increases randomly), which makes it highly unlikely to be the correct pattern.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series Completion 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 analyze sequences and identify patterns is analogous to recognizing trends in a patient's vital signs or lab results over time.
For example, a nurse observes a patient's heart rate at 8 AM (70 bpm), 10 AM (75 bpm), 12 PM (80 bpm), and needs to anticipate the trend to assess the patient's stability.

How to Approach the Question

First, write down the series and identify the position of the missing number.
Calculate the difference between each pair of known, consecutive numbers. In this case, -7 - (-15) = 8 and 26 - 14 = 12.
Observe the sequence of differences you've found. Here, it starts at 8 and ends at 12, suggesting an increasing pattern.
Form a hypothesis about the complete sequence of differences. A simple hypothesis is that the differences are consecutive or near-consecutive integers.
Test the given options. For each option, fill in the blank and calculate the full sequence of differences.
Select the option that results in the most logical and consistent pattern. In this case, choosing 3 gives the differences [8, 10, 11, 12], which is a clear increasing sequence.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

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