What will come in place of the question mark in the following numerical series?
6, 9, 14, 21, 30, ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 41
When a number series grows by uneven steps, look at the difference between each pair of terms. Here the differences are the odd numbers in order:
\(9-6=3\)
\(14-9=5\)
\(21-14=7\)
\(30-21=9\)
The next difference is 11, so the missing term is \(30+11=41\).
The same series can be read as \(n^2+5\) for \(n=1, 2, 3, \ldots\): \(1+5=6\), \(4+5=9\), \(9+5=14\), \(16+5=21\), \(25+5=30\), and \(36+5=41\).