document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=656238>Question 656238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many terms of the arithmetic series 1491 + 1484+1477+... are needed to give a sum of zero </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #409413 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=409413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In this case, a1 = 1491 and d = -7  (since 1484-1491 = -7)\r<BR>\n" );
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document.write( "We want Sn = 0, so let's all plug this into the formula below\r<BR>\n" );
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document.write( "Sn = (n*(2*a1 + d*(n-1)))/2\r<BR>\n" );
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document.write( "to get\r<BR>\n" );
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document.write( "0 = (n*(2*1491 + (-7)*(n-1)))/2\r<BR>\n" );
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document.write( "and now let's solve for n.\r<BR>\n" );
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document.write( "0 = (n*(2*1491 + (-7)*(n-1)))/2\r<BR>\n" );
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document.write( "0 = (n*(2982 -7n + 7))/2\r<BR>\n" );
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document.write( "0 = (n*(-7n + 2989))/2\r<BR>\n" );
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document.write( "0 = (-7n^2 + 2989n)/2\r<BR>\n" );
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document.write( "0 = -7n^2 + 2989n\r<BR>\n" );
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document.write( "-7n^2 + 2989n = 0\r<BR>\n" );
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document.write( "-7n(n - 427) = 0\r<BR>\n" );
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document.write( "-7n = 0 or n - 427 = 0\r<BR>\n" );
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document.write( "n = 0 or n = 427\r<BR>\n" );
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document.write( "Ignore the solution n = 0 since you can't have 0 terms.\r<BR>\n" );
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document.write( "So you need 427 terms. </SPAN>\n" );
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