Directions: In the following question a number series is given. After the series, a number is given followed by (a), (b) and (c). You have to complete the series starting with the number given following the sequence of the given series. Then answer the question given below it.

Which of the following numbers will come in place of (c)?

4 5 22 201

7 (a) (b) (c)

4	5	22	201
7	(a)	(b)	(c)

Appeared in: AIIMS Raipur NO- 2019 (shift 3rd)

Explanation

The series follows the pattern: Previous Term × (n²) + n, where 'n' increments by 1 for each subsequent term (1, 2, 3, ...).
The first series confirms this pattern: 4 × (1²) + 1 = 5; 5 × (2²) + 2 = 22; 22 × (3²) + 3 = 201.
Applying this to the second series, which starts with 7, we find the subsequent terms.
The second term (a) is calculated as 7 × (1²) + 1 = 8.
The third term (b) is calculated as 8 × (2²) + 2 = 34.
The fourth term (c) is calculated as 34 × (3²) + 3 = 306 + 3 = 309.

Option A: This value does not fit the established pattern. It might result from a calculation error, such as miscalculating 34 × 9.
Option B: This value does not follow the series logic. It might be a result of rounding down or an arithmetic mistake, for instance, calculating 34 × 9 as 297 and then adding 3.
Option C: This option is incorrect because the correct answer, 309, is available as option D. This option is only chosen when no other provided option is correct.

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 this is a numerical reasoning question, strong analytical and pattern-recognition skills are essential for nurses.
Nurses use similar logical deduction for interpreting patient data, recognizing trends in vital signs, and calculating medication dosages accurately.
What if? - What if the pattern was Previous Term × n + n? Then (a) would be 7×1+1=8, (b) would be 8×2+2=18, and (c) would be 18×3+3=57. This highlights the importance of correctly identifying the underlying pattern before proceeding.

How to Approach the Question

First, analyze the given complete series (4, 5, 22, 201) to identify the mathematical relationship between consecutive numbers.
Test common patterns: addition, subtraction, multiplication, division, squares, cubes, or a combination of these operations.
In this case, the pattern is Previous Term × (n²) + n, where n starts at 1. Verify this pattern for all terms in the first series.
Once the pattern is confirmed, apply the exact same logic to the second series, starting with the number 7.
Calculate the values for (a), (b), and finally (c) step-by-step.
Match the calculated value for (c) with the given options.

Concept Tested & Keywords

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Practise the full AIIMS Raipur NO- 2019 (shift 3rd)

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