Discussion

What should come in place of the question mark in the following series?

24, 536, 487, 703, 678, ?

Answer: C

The missing number is 742.

The differences alternate between cubes added and squares subtracted, each base falling by one:

\[ \begin{aligned} 24 + 8^{3} &= 536,\ 536 - 7^{2} = 487 \\ 487 + 6^{3} &= 703,\ 703 - 5^{2} = 678 \\ 678 + 4^{3} &= 742 \end{aligned} \]

736 and 836 would need differences of 58 and 158, and 842 a difference of 164; none is the cube of 4 (64), which the pattern requires next.

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