An algebra problem by Rahil Sehgal

Algebra Level pending

The first term of a sequence is 2014. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the 2014๐‘กโ„Ž term of the sequence?


The answer is 370.

Rahil Sehgal by Rahil Sehgal , 20, India

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1 solution

Viki Zeta
Mar 10, 2017

a = 2014 , a 2 = 2 3 + 0 3 + 1 3 + 4 3 = 370 a 3 = 3 3 + 0 3 + 7 3 = 73 a 4 = 7 3 + 3 3 = 370 Similarly, a 5 = 73 a 6 = 370 a 2 n = 370 , a 2 n + 1 = 73 2014 = 2 โˆ— 1007 a 2014 = a 2 ร— 1007 = 370 a = 2014,\\ a_2 = 2^3 + 0^3 + 1^3 + 4^3 = 370 \\ a_3 = 3^3 + 0^3 + 7^3 = 73 \\ a_4 = 7^3 + 3^3 = 370\\ \text{Similarly, } \\ a_5 = 73 \\ a_6 = 370 \\ a_{2n} = 370, ~ a_{2n+1} = 73 \\ 2014 = 2 * 1007 \\ \boxed{a_{2014} = a_{2 \times 1007} = 370}\\

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