Discussion
The missing number in the following sequence will be
2, 9, 28, ....., 126
Answer: D
The missing number is 65.
Each term is one more than a cube:
\[ \begin{aligned} 2 &= 1^{3} + 1,\quad 9 = 2^{3} + 1,\quad 28 = 3^{3} + 1 \\ 65 &= 4^{3} + 1,\quad 126 = 5^{3} + 1 \end{aligned} \]
so the gap is filled by \(4^{3} + 1 = 65\). 63 is \(4^{3} - 1\), and 57 and 53 do not fit the pattern; the differences 7, 19, 37, 61 also confirm 65, since they rise by 12, 18, 24.
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