Discussion
What should come at the place of question mark (?) in the following number series?
-1, 2, 7, 14, 23, ?
Answer: B
The next term is 34.
The differences between successive terms are consecutive odd numbers:
\[ \begin{aligned} 2 - (-1) &= 3,\ 7 - 2 = 5 \\ 14 - 7 &= 7,\ 23 - 14 = 9 \end{aligned} \]
The next difference is 11, so the missing term is 23 + 11 = 34. Equivalently, the terms are \(n^2 - 2\) for n = 1, 2, 3 and so on, and \(6^2 - 2 = 34\). 36 and 35 come from adding 13 or 12 instead of 11.
The formula checks every given term: 1 - 2 = -1, 4 - 2 = 2, 9 - 2 = 7, 16 - 2 = 14 and 25 - 2 = 23. Option C, 32, repeats the difference of 9.
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