An algebra problem by Puneet Pinku
Algebra
Level
3
The first term of a sequence is 2005. Each succeding term is the sum of the cubes of the digits of the digits of the previous term. What is the 2005th term of the sequence?
250
100
125
175
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1 solution
Performing this operation several times yields the results of 133 for the second term, 55 for the third term, and 250 for the fourth term. The sum of the cubes of the digits of 250 equal 133, a complete cycle. The cycle is... excluding the first term, the 2nd, 3rd and 4th terms will equal 133, 55, and 250, following the fourth term. Any term number that is equivalent to 1{mod 3) will produce a result of 250.