Problem:
The first term of a sequence is 2005. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the term of the sequence?
Answer Choices:
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E.
Solution:
The sequence begins Thus after the initial term 2005, the sequence repeats the cycle . Because , the term is the same as the last term of the repeating cycle, .
The problems on this page are the property of the MAA's American Mathematics Competitions