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1) 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, 1^3 + 3^3 = 28 the second term is  Find the 100th term.

2) In a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh term is equal to 6. Find the sum of all ten terms.

Feb 20, 2020

#1
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Here is the answer  to  (2)

https://web2.0calc.com/questions/help_66938   Feb 20, 2020
#2
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1) 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, 1^3 + 3^3 = 28 the second term is  Find the 100th term.

Let's see if  we can discover a pattern .....

Term       Value

2            28

3           520

4           133

5            55

6           250   (0)

7           133   (1)

8            55    (2)

9           250   (0)

Note  that  the  series  repeats  starting  at  term 6 and has  a length of 3  before it begins again

And  note  that

6 mod  3  = (0)

7 mod 3  =  (1)

8 mod 3  =  (2)

9 mod (3)  = (0)

So

100 mod 3   = (1)

So....the 100th term  =  133   Feb 20, 2020