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Number Theory Level 2

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 2015th term of the sequence?

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The answer is 370.

Ganeshkumar Ashokavardhanan by Ganeshkumar Ashokavardh… , 22

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2 solutions

Ratnadip Kuri
Jan 16, 2015

step 1: second term = 2 3 2^3 + 0 3 0^3 + 1 3 1^3 + 4 3 4^3 = 73

step 2: Third term = 7 3 7^3 + 3 3 3^3 =370

In third term non-zero digits are 3 and 7 which is same with second term. So 370 always return result 370. It doesn't matter what successive position of the number in the sequence. So, 2015th term is also 370.

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Sudoku Subbu
Jan 16, 2015

when we go to the second term its 8+0+1+64=73 , the third term is 343 + 27=370 , again fourth , fifth , sixth , . . . . . . . . . . . . . . . . . 2015th term are 370 therefore the 2015th term is 370

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Correct reasoning!

Ganeshkumar Ashokavardhanan - 6 years, 4 months ago

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