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Question 1

Observe the following sequence. What is the 100th term? $$7, 8, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3, \ldots$$

Solution

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Grouping the terms from the third term onward in blocks of three gives $$1, 0, 0$$ then $$1, 0, 1$$ then $$1, 0, 2$$ then $$1, 0, 3$$, so each block repeats the pair $$1, 0$$ followed by a number that increases by 1 in every block. Continuing this repeating structure out to the 100th position gives a value of 3.

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