What will come in place of Question mark (?) in the following number series?
3, 4.5, 9, 22.5, 67.5, (?), 945

Appeared in: DHS 2018 shift 1st

Explanation

The series follows a multiplicative pattern where the multiplier increases by 0.5 at each step.
The sequence of multipliers is 1.5, 2, 2.5, 3, and so on.
To find the missing term, the previous term (67.5) must be multiplied by the next factor in the sequence, which is 3.5.
The calculation is: 67.5 × 3.5 = 236.25.
To verify, multiplying 236.25 by the next factor (4) gives 945, which is the last term in the series, confirming the pattern.

Option A: This value does not result from multiplying 67.5 by 3.5. It breaks the established mathematical progression of the series.
Option C: This is an incorrect calculation and does not fit the logical sequence of multiplying by factors that increase by 0.5.
Option D: This number is significantly lower than expected and does not follow the exponential growth demonstrated by the series pattern.

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, logical reasoning and pattern recognition are essential skills for nurses.
These skills are applied in interpreting trends in patient vital signs, recognizing patterns in symptoms, and making quick, logical decisions in patient care.
For example, a nurse might notice a progressive, patterned drop in blood pressure over several hours, prompting a specific intervention.

How to Approach the Question

First, examine the relationship between the first few numbers in the series to identify a potential pattern.
Calculate the difference (subtraction) and the ratio (division) between consecutive terms.
In this case, dividing the second term by the first (4.5 ÷ 3 = 1.5) and the third by the second (9 ÷ 4.5 = 2) reveals a multiplicative pattern.
Identify how the multiplier changes with each step. Here, it increases by 0.5 (1.5, 2, 2.5, 3...).
Apply the next logical step in the pattern (multiplying by 3.5) to the last known number (67.5) to find the missing term.
Verify your answer by applying the subsequent step in the pattern to your result to see if it matches the final number in the series (236.25 × 4 = 945).

Concept Tested & Keywords

QSPjdl722dVat2iRwzE0Bh

Practise the full DHS 2018 shift 1st

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