The Fibonacci Sequence

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The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21... starts with two 1's, and each term afterward is the sum of its two predecessors.

Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?

Just write out their units digits, and mark the digits that appear for the first time.

(1), 1, (2), (3), (5), (8), 3, 1, (4), 5, (9), 4, 3, (7), (0), ...
Therefore, 6 is the last to appear.

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