What is the next number in this sequence? 1,3, 8, 19, 42, 89, ?

Appeared in: AIIMS Delhi NO - 2017

Explanation

The sequence follows the rule where the next term is calculated as (Previous Term × 2) + n, where 'n' is an integer that starts at 1 and increments by 1 for each subsequent term.
The first term is 1.
The second term is (1 × 2) + 1 = 3.
The third term is (3 × 2) + 2 = 8, and so on.
Applying this rule to the last known term, 89, requires multiplying it by 2 and adding the next integer in the sequence, which is 6.
The calculation is (89 × 2) + 6 = 178 + 6 = 184.

Option A: 108 is incorrect. This result might be obtained through a miscalculation or by applying an incorrect pattern, such as adding a constant or misinterpreting the incremental addition.
Option C: 167 is incorrect. This number does not fit the established pattern of (x * 2) + n. For example, (89 * 2) = 178, which is already greater than 167.
Option D: 97 is incorrect. This would only be a small increase from 89 and does not follow the accelerating growth of the sequence.

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, this type of logical reasoning problem assesses critical thinking and pattern recognition skills.
These skills are essential for nurses in clinical practice for tasks like interpreting trends in vital signs, recognizing subtle changes in a patient's condition, and making quick, logical decisions.
What if the pattern was simply doubling? If the pattern was just x * 2, the sequence would be 1, 2, 4, 8, 16, 32, etc. The complexity here comes from the second operation (adding an increasing number).

How to Approach the Question

First, carefully examine the sequence of numbers provided: 1, 3, 8, 19, 42, 89.
Try to identify a simple arithmetic relationship between consecutive numbers (e.g., addition, subtraction, multiplication, or division by a constant). Notice that the gap between numbers is increasing, suggesting multiplication is involved.
Test a combined operation. For example, see how you get from 1 to 3. It could be 1+2 or (1*2)+1. Then check if the same rule applies to get from 3 to 8. 3+5 is different. But (3*2)+2 = 8. This reveals a potential pattern.
Verify the pattern (Previous Term × 2) + n for the entire sequence, where 'n' increases by 1 each time.
Once the pattern is confirmed, apply it to the last number (89) to calculate the missing term.
Alternatively, calculate the differences between consecutive terms, and then calculate the differences of those differences to find a simpler underlying pattern.

Concept Tested & Keywords

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Practise the full AIIMS Delhi NO - 2017

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