Q.5 In the sequence 6, 9, 14, x, 30, 41, a possible value of đť‘Ą is
(A) 25
(B) 21
(C) 18
(D) 20
Pattern Analysis
Calculate differences: 9 – 6 = 3, 14 – 9 = 5, x – 14 = ?, 30 – x = ?, 41 – 30 = 11. The differences 3, 5, 11 suggest an arithmetic progression of odd numbers increasing by 2 each time. Thus, next differences are 7 (14 + 7 = 21), 9 (21 + 9 = 30), confirming consistency.
Option Breakdown
(A) 25
Gives differences 3, 5, 11 (14+11=25), 5 (25+5=30), 11. No consistent odd number progression (jumps irregularly). Incorrect.
(B) 21
Yields 3, 5, 7 (14+7=21), 9 (21+9=30), 11. Perfect match for consecutive odds: 3,5,7,9,11. Correct.
(C) 18
Produces 3, 5, 4 (14+4=18), 12 (18+12=30), 11. No logical pattern in differences. Incorrect.
(D) 20
Results in 3, 5, 6 (14+6=20), 10 (20+10=30), 11. Differences lack progression. Incorrect.
Exam Relevance
This question appeared in GATE CS 2024 Set 2 (General Aptitude). Such number series test pattern recognition, vital for CSIR NET quantitative sections too. Practice identifies odd number additions quickly.
Correct Answer: (B) 21
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