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.)

Algebra ->  Sequences-and-series -> 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.)      Log On


   

Question 821193: Find the sum of the first 60 terms of the sequence below.
15,17,2,-15,-17
(Where a+sub%28n%29=+a+sub+%28n-1%29-a+sub+%28n-2%29 and n is less than or equal to 3.)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It is highlight%28%220%22%29 ,highlight%28zilch%29 ,highlight%28nada%29 .
The first term is a%5B1%5D=15 .
The second term is a%5B2%5D=17 .
The formula given to calculate each term starting with the third term, a%5B3%5D is
a%5Bn%5D=+a%5Bn-1%5D-a%5Bn-2%5D for n%3E=3 (n is greater than or equal to 3).
So for n=3 we have a%5B3%5D=a%5B2%5D-a%5B1%5D=17-15=2 ,
for n=4 we have a%5B4%5D=a%5B3%5D-a%5B2%5D=2-17=-15 ,
for n=45 we have a%5B5%5D=a%5B4%5D-a%5B3%5D=-15-2=-17 , 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 a%5B6%5D=-2 , a%5B7%5D=15 , a%5B8%5D=17 , and so on.
Have you ever read the book Hopscotch by Julio Cortázar?
You could try your algebra to prove that a%5Bn%2B6%5D=a%5Bn%5D .
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 n,
you will be adding packets of 6 terms that add up to 0,
and if n 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 n 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 a%5Bn%5D .
For greater than or equal to, we use >= .
For not equal to, we use <> .