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The first term of a sequence is 13. Starting with the second term, each term is the sum of the cubes of the digits in the previous term. For example, the second term is  Find the 100th term.

 Mar 1, 2021
 #1
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Let's see  if we have a pattern

 

Term   

1  = 13 

2  =  1^3  + 3^3   =  28

3  =   2^3  + 8^3   =  520

4  =  5^3 +  2^3   =  133

5  = 1^3 + 3^3 + 3^3  = 55

6  = 5^3 + 5^3  =  250

7  = 2^3 + 5^3  =  133

8 = 1^3 + 3^3 + 3^3  =  55

9 = 5^3 + 5^3  =  250

 

Notice that.....after  the 3rd term, the pattern repeats  in cycles  of  3

The 100th term  is   100 mod 3 = 1  =   1st term  in the pattern =  133

 

 

cool cool cool

 Mar 1, 2021

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