SOLUTION: Find the sum of the first 60 terms of the sequence below. 15,17,2,-15,-17 (Where {{{a sub(n)= a sub (n-1)-a sub (n-2)}}} and n is less than or equal to 3.)

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Question 821193: Find the sum of the first 60 terms of the sequence below.
15,17,2,-15,-17
(Where and n is less than or equal to 3.)
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
It is , , .
The first term is .
The second term is .
The formula given to calculate each term starting with the third term, is
for (n is greater than or equal to 3).
So for we have ,
for we have ,
for we have , and so on.

If you look very closely, or if you calculate a few more terms beyond the 5 terms given, you realize that you are sort of going around in circles.
You will see that , , , and so on.
Have you ever read the book Hopscotch by Julio Cortázar?
You could try your algebra to prove that .
The ordered set of the first 6 terms is
the same as
the ordered set of the next 6 terms,
the same as
the ordered set of the next 6 terms,
and so on.
The first six terms, 15,17,2,-15,-17,-2, add up to 0.
So do terms number 7 through 12,
and terms number 13 through 18,
and so on.
In general if you start with the first term, and add all the terms up to a term number ,
you will be adding packets of 6 terms that add up to 0,
and if is not a multiple of 6,
you will add a few more terms at the end.
How many terms are you adding at the end?
The remainder of dividing the number by 6.

NOTE:
Good try at using the symbols from this site.
For subscripts, we wrap the subscript in square brackets, as in a[n] for .
For greater than or equal to, we use >= .
For not equal to, we use <> .
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