Complete the following series- 2, 3, 18, 115, 854, ...

Appeared in: Haryana CHO - 2022

Explanation

The series follows the pattern: Next Term = (Previous Term × N) + N², where N represents consecutive odd numbers starting from 1 (1, 3, 5, 7, 9...).
The first term is 2.
To get the second term: (2 × 1) + 1² = 3.
To get the third term: (3 × 3) + 3² = 18.
To get the fourth term: (18 × 5) + 5² = 115.
To get the fifth term: (115 × 7) + 7² = 854.

Option A: This value does not fit the established mathematical pattern of the series.
Option C: This value is incorrect. It deviates from the logical progression determined by the formula (Previous Term × N) + N².
Option D: This value is mathematically incorrect according to the series' rule. The calculation (854 × 9) + 9² yields 7767, not 7967.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests logical reasoning and the ability to identify complex mathematical patterns in a number series as background academic context rather than a clinical decision trigger.
While this is a general intelligence question, such problem-solving skills are foundational for nurses.
Nurses frequently use mathematical skills for tasks like calculating medication dosages, titrating IV drips, and interpreting lab values, all of which require precision and logical thinking.
What if the pattern was simpler, like just multiplying by consecutive odd numbers? The series would be 2, 6 (2x3), 30 (6x5), 210 (30x7), etc. The ability to test different logical patterns is key.

How to Approach the Question

First, analyze the relationship between consecutive numbers in the series (2, 3, 18, 115, 854).
Observe the difference or ratio between terms. Notice that the increase is not arithmetic or simply geometric; it grows very rapidly, suggesting multiplication and possibly other operations.
Test for patterns involving multiplication, addition/subtraction, squares, or cubes. For example, check 3/2, 18/3, 115/18.
Try to find a rule that connects each term to the next. For instance, 3 = 21 + 1. Let's test this idea: 18 = 3? + ?. The numbers are growing, so let's try consecutive odd numbers: 18 = 33 + 9 = 33 + 3². This looks promising.
Verify the identified pattern: (Previous Term × N) + N² with N as consecutive odd numbers (1, 3, 5, 7...).
Apply the confirmed pattern to the last known term (854) to find the missing number in the series.

Concept Tested & Keywords

Concept Tested: This question tests logical reasoning and the ability to identify complex mathematical patterns in a number series.
Stem keywords: number series, complete the series, pattern recognition
Lead-in keywords: Complete the following series

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Practise the full Haryana CHO - 2022

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