document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=656236>Question 656236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sum of the terms of an arithmetic series is 234, and the middle term is 26, find the number of terms in the series. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #409424 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=409424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The middle term is 26, so the first term is a1 = 26 - k*d for some common difference d and some number of terms before the middle term k.\r<BR>\n" );
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document.write( "The middle term is 26, so the nth term (or the last term) is an = 26 + k*d for some common difference d and some number of terms before the middle term k.\r<BR>\n" );
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document.write( "Now use the arithmetic sequence partial sum formula.\r<BR>\n" );
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document.write( "Sn = n*(a1 + an)/2\r<BR>\n" );
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document.write( "Sn = n*((26 - k*d) + (26 + k*d))/2\r<BR>\n" );
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document.write( "Sn = n*(26 - k*d + 26 + k*d)/2\r<BR>\n" );
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document.write( "Sn = n*(52)/2\r<BR>\n" );
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document.write( "234 = n*(52)/2\r<BR>\n" );
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document.write( "234*2 = 52n\r<BR>\n" );
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document.write( "468 = 52n\r<BR>\n" );
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document.write( "52n = 468\r<BR>\n" );
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document.write( "n = 468/52\r<BR>\n" );
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document.write( "n = 9\r<BR>\n" );
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document.write( "So there are 9 terms in the sequence.\r<BR>\n" );
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document.write( "Unfortunately, no unique sequence has 9 terms where they sum up to 234 (with 26 in the middle), but here are a few sequences that fit this description:\r<BR>\n" );
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document.write( "2 + 8 + 14 + 20 + 26 + 32 + 38 + 44 + 50 = 234\r<BR>\n" );
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document.write( "6 + 11 + 16 + 21 + 26 + 31 + 36 + 41 + 46 = 234\r<BR>\n" );
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document.write( "10 + 14 + 18 + 22 + 26 + 30 + 34 + 38 + 42 = 234\r<BR>\n" );
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document.write( "30 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 22 = 234\r<BR>\n" );
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document.write( "74 + 62 + 50 + 38 + 26 + 14 + 2 - 10 - 22 = 234\r<BR>\n" );
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document.write( "There are infinitely more sequences that fit this description. </SPAN>\n" );
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