Complete the series: 7, 10, 16, 28, 52, ?

Appeared in: DSSSB 6 September 2024

Explanation

The series follows a pattern where the difference between consecutive numbers doubles at each step.
The initial difference is 10 - 7 = 3.
The subsequent differences are 6 (3×2), 12 (6×2), and 24 (12×2).
To find the next number, the next difference must be 24 × 2 = 48.
Adding this difference to the last term gives the answer: 52 + 48 = 100.
An alternative pattern is to multiply the previous number by 2 and then subtract 4: (52 × 2) - 4 = 104 - 4 = 100.

Option A: This would mean the difference is 36 (88 - 52). This breaks the established pattern of doubling the previous difference, which requires the next difference to be 48 (24 x 2).
Option B: This implies a difference of 44 (96 - 52). The correct pattern requires the difference to be 48, which is double the previous difference of 24.
Option D: This is the result of only multiplying the last number by 2 (52 × 2 = 104) but forgetting to subtract 4, which is a necessary step in the alternative pattern of (Term × 2) - 4.

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, number series problems test logical and analytical reasoning skills.
These skills are crucial for nurses in various situations, such as calculating drug dosages, interpreting trends in vital signs, and managing patient care schedules efficiently.
What if? - If the pattern was simply adding the two previous differences (a Fibonacci-like sequence for the differences), the next difference would be 12 + 24 = 36, and the next term would be 52 + 36 = 88. This highlights the importance of correctly identifying the underlying pattern.

How to Approach the Question

First, write down the series and look for an obvious pattern.
Calculate the differences between consecutive terms: 10-7=3, 16-10=6, 28-16=12, 52-28=24.
Analyze the sequence of differences (3, 6, 12, 24) to find its pattern. Here, each difference is double the previous one.
Determine the next difference in the sequence: 24 × 2 = 48.
Add this next difference to the last term of the original series to find the missing number: 52 + 48 = 100.
As a check, look for alternative patterns. For instance, test if a combination of multiplication/division and addition/subtraction applies to all terms. In this case, (Term × 2) - 4 also works.

Concept Tested & Keywords

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Practise the full DSSSB 6 September 2024

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