Discussion
The list below is incomplete by exactly one term. Identify the pattern, then choose the number that belongs at the question mark.
1, 4, 10, 20, 35, ?
Answer: C
Correct answer: 56
The gaps are 3, 6, 10, 15, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the running total of the triangular numbers: position 1 gives 1 and position 5 gives 35. The next position is 6, which gives 56. As a check, the same rule applied to the earlier positions reproduces 1, 4, 10, 20, 35 exactly, so it accounts for every term shown and not merely the last. Each triangular number is the sum of all the whole numbers up to its position, which gives a direct formula.
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