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One entry is missing from the sequence set out below. Find the rule and name the term that completes the run.
7, 26, 63, 124, ?

  • A.216
  • B.214
  • C.276
  • D.215

Answer: B

Correct answer: 215

The gaps are 19, 37, 61, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is one less than the cube of its position: position 2 gives 7 and position 5 gives 124. The next position is 6, which gives 215. As a check, the same rule applied to the earlier positions reproduces 7, 26, 63, 124 exactly, so it accounts for every term shown and not merely the last. Adding the position number to a cube leaves the growth dominated by the cube, so the family is identified from the largest terms.

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