Find the missing number in the following number series?

243,-81,______,-9,3

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The question requires finding a missing term in a number series.
The series follows a geometric progression where each term is the previous term divided by a common ratio.
To find the second term (-81) from the first (243), we divide by -3 (243 / -3 = -81).
To find the fifth term (3) from the fourth (-9), we divide by -3 (-9 / -3 = 3).
Applying this rule to find the missing term: -81 ÷ (-3) = 27.
The correct missing term that fits the pattern is 27.

Option A: This option does not follow the mathematical rule governing the series. The pattern is division by -3, not an arbitrary subtraction or addition that would result in 33.
Option C: This option has both the incorrect value and the incorrect sign. The series alternates between positive and negative values, and the missing term should be positive.
Option D: This option has the correct numerical value but the incorrect sign. The rule of division states that dividing a negative number by a negative number results in a positive number (-81 ÷ -3 = +27).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to identify patterns in a number series, specifically a geometric progression as background academic context rather than a clinical decision trigger.
This is a general intelligence and reasoning question, not directly related to clinical nursing practice.
Skills in logical reasoning and pattern recognition are valuable for nurses in problem-solving and critical thinking, such as identifying trends in a patient's vital signs or lab results.
What if the series was 243, -81, 27, 9, 3? The pattern would be inconsistent. The first two steps involve dividing by -3, but the step from 27 to 9 involves dividing by +3, indicating a broken or more complex pattern.

How to Approach the Question

First, examine the relationship between the first two numbers (243 and -81) to form a hypothesis about the pattern.
Notice the change in both value and sign. 243 is much larger than 81, suggesting division or subtraction. The sign change suggests multiplication or division by a negative number.
Test the hypothesis: 243 ÷ (-3) = -81. This works.
Check if this rule applies to other known parts of the series. Look at the end: -9 and 3. Test the rule: -9 ÷ (-3) = 3. The rule is consistent.
Apply the confirmed rule to find the missing term. The term before the blank is -81. Calculate: -81 ÷ (-3) = 27.
Select the option that matches your calculated result.

Concept Tested & Keywords

Concept Tested: This question tests the ability to identify patterns in a number series, specifically a geometric progression.
Stem keywords: missing number, number series
Lead-in keywords: Find

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Practise the full DSSSB -28 August 2019 (Shift-2)

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