In the sequence 6, 9, 14, \(x\), 30, 41, a possible value of \(x\) is
Answer
(B)
Explanation
Look at the gaps between terms: \(9 - 6 = 3\) and \(14 - 9 = 5\). They are consecutive odd numbers, so the next gaps should be 7, 9 and 11:
\[14 + 7 = 21,\quad 21 + 9 = 30,\quad 30 + 11 = 41.\]
This reproduces the given 30 and 41, so \(x = 21\). Equivalently, the terms are \(n^{2} + 5\) for \(n = 1, 2, \ldots, 6\).
The other values break the pattern: 25, 18 and 20 leave gaps of 11 and 5, 4 and 12, or 6 and 10 around \(x\).
Answer: B