document.write( "Question 821193: Find the sum of the first 60 terms of the sequence below.
\n" ); document.write( "15,17,2,-15,-17
\n" ); document.write( "(Where $\"a+sub%28n%29=+a+sub+%28n-1%29-a+sub+%28n-2%29\"$ and n is less than or equal to 3.) \n" ); document.write( "

Algebra.Com's Answer #493970 by KMST(5328) $\"\"$ $\"About$

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It is $\"highlight%28%220%22%29\"$ , $\"highlight%28zilch%29\"$ , $\"highlight%28nada%29\"$ .
\n" ); document.write( "The first term is $\"a%5B1%5D=15\"$ .
\n" ); document.write( "The second term is $\"a%5B2%5D=17\"$ .
\n" ); document.write( "The formula given to calculate each term starting with the third term, $\"a%5B3%5D\"$ is
\n" ); document.write( " $\"a%5Bn%5D=+a%5Bn-1%5D-a%5Bn-2%5D\"$ for $\"n%3E=3\"$ (n is greater than or equal to 3).
\n" ); document.write( "So for $\"n=3\"$ we have $\"a%5B3%5D=a%5B2%5D-a%5B1%5D=17-15=2\"$ ,
\n" ); document.write( "for $\"n=4\"$ we have $\"a%5B4%5D=a%5B3%5D-a%5B2%5D=2-17=-15\"$ ,
\n" ); document.write( "for $\"n=45\"$ we have $\"a%5B5%5D=a%5B4%5D-a%5B3%5D=-15-2=-17\"$ , and so on.
\n" ); document.write( "
\n" ); document.write( "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.
\n" ); document.write( "You will see that $\"a%5B6%5D=-2\"$ , $\"a%5B7%5D=15\"$ , $\"a%5B8%5D=17\"$ , and so on.
\n" ); document.write( "Have you ever read the book Hopscotch by Julio Cortázar?
\n" ); document.write( "You could try your algebra to prove that $\"a%5Bn%2B6%5D=a%5Bn%5D\"$ .
\n" ); document.write( "The ordered set of the first 6 terms is
\n" ); document.write( "the same as
\n" ); document.write( "the ordered set of the next 6 terms,
\n" ); document.write( "the same as
\n" ); document.write( "the ordered set of the next 6 terms,
\n" ); document.write( "and so on.
\n" ); document.write( "The first six terms, 15,17,2,-15,-17,-2, add up to 0.
\n" ); document.write( "So do terms number 7 through 12,
\n" ); document.write( "and terms number 13 through 18,
\n" ); document.write( "and so on.
\n" ); document.write( "In general if you start with the first term, and add all the terms up to a term number $\"n\"$ ,
\n" ); document.write( "you will be adding packets of 6 terms that add up to 0,
\n" ); document.write( "and if $\"n\"$ is not a multiple of 6,
\n" ); document.write( "you will add a few more terms at the end.
\n" ); document.write( "How many terms are you adding at the end?
\n" ); document.write( "The remainder of dividing the number $\"n\"$ by 6.
\n" ); document.write( "
\n" ); document.write( "NOTE:
\n" ); document.write( "Good try at using the symbols from this site.
\n" ); document.write( "For subscripts, we wrap the subscript in square brackets, as in a[n] for $\"a%5Bn%5D\"$ .
\n" ); document.write( "For greater than or equal to, we use >= .
\n" ); document.write( "For not equal to, we use <> . \n" ); document.write( "

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