From the following options, choose the missing number to complete the given series. 2, 5, 10, 17, ______

Appeared in: CGHS SSC - 2018

Explanation

The series follows the pattern of n2 + 1, where 'n' represents the term's position in the sequence.
The first term is 12 + 1 = 2.
The second term is 22 + 1 = 5.
The third term is 32 + 1 = 10.
The fourth term is 42 + 1 = 17.
Following this pattern, the fifth and missing term is 52 + 1 = 25 + 1 = 26.

Option B: This is incorrect. If the next term were 27, the difference from the previous term (17) would be 10. This breaks the established pattern of adding consecutive odd numbers (3, 5, 7, ...).
Option C: This is incorrect. A value of 28 would mean the difference is 11 (28 - 17). While 11 is an odd number, it is not the next consecutive odd number after 7; the pattern requires the next difference to be 9.
Option D: This is incorrect. A value of 21 would imply a difference of 4 (21 - 17). This breaks the pattern of adding odd numbers and also the pattern of the differences increasing.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Identifying the pattern in a numerical series as background academic context rather than a clinical decision trigger.
This type of logical reasoning question assesses problem-solving and pattern recognition skills.
While not directly clinical, these analytical skills are crucial for nurses in interpreting patient data, recognizing trends in vital signs, and making quick, logical decisions in high-pressure situations.
What if the series was 2, 6, 12, 20? The pattern would be n2 + n. The next term would be 52 + 5 = 30. This highlights the importance of testing different common patterns (n2, n2+1, n2+n, etc.) to develop flexible problem-solving abilities.

How to Approach the Question

First, carefully examine the given series: 2, 5, 10, 17.
Calculate the difference between consecutive terms to check for a simple arithmetic pattern. (5-2=3), (10-5=5), (17-10=7).
Recognize that the differences (3, 5, 7) are consecutive odd numbers, so the next difference should be 9.
Add this next difference to the last known term of the series: 17 + 9 = 26.
As a confirmation, test for other common patterns like squares or cubes. Notice that each term is one more than a perfect square: 12+1=2, 22+1=5, 32+1=10, 42+1=17.
Apply this n2 + 1 rule to find the fifth term: 52 + 1 = 26. Since both methods yield the same result, you can be confident in the answer.

Concept Tested & Keywords

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Practise the full CGHS SSC - 2018

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