+14 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.
+129852 Here is the answer to (2)
https://web2.0calc.com/questions/help_66938
+129852 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
