document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692570>Question 692570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arithmetic series has a third term of 0. The sum of the first 15 terms is – 300. What is the first term? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427076 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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/cgi-bin/show-face.mpl?user=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=427076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "An arithmetic series has a third term of 0. The sum of the first 15 terms is – 300. What is the first term?\r<BR>\n" );
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document.write( "Formula for d, or the common difference in a series: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28a%5Bn%5D+-+a%5B1%5D%29%2F%28n+-+1%29 ALIGN=MIDDLE  ALT=\"d+=+%28a%5Bn%5D+-+a%5B1%5D%29%2F%28n+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0, and n = 3\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28a%5Bn%5D+-+a%5B1%5D%29%2F%28n+-+1%29 ALIGN=MIDDLE  ALT=\"d+=+%28a%5Bn%5D+-+a%5B1%5D%29%2F%28n+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%280+-+a%5B1%5D%29%2F%283+-+1%29 ALIGN=MIDDLE  ALT=\"d+=+%280+-+a%5B1%5D%29%2F%283+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28-+a%5B1%5D%29%2F2 ALIGN=MIDDLE  ALT=\"d+=+%28-+a%5B1%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ eq (i)\r<BR>\n" );
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document.write( "Formula for sum of a series of numbers, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B15%5D ALIGN=MIDDLE  ALT=\"S%5B15%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = - 300 ; and n = 15\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B15%5D+=+%2815%2F2%29%282a%5B1%5D+%2B+%2815+-+1%29d%29 ALIGN=MIDDLE  ALT=\"S%5B15%5D+=+%2815%2F2%29%282a%5B1%5D+%2B+%2815+-+1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+300+=+7.5%282a%5B1%5D+%2B+14d%29 ALIGN=MIDDLE  ALT=\"-+300+=+7.5%282a%5B1%5D+%2B+14d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+300+=+15a%5B1%5D+%2B+105d ALIGN=MIDDLE  ALT=\"-+300+=+15a%5B1%5D+%2B+105d\"   DISABLED_style= \"max-width:90%; height:auto;\" > --- eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+300+=+15a%5B1%5D+%2B+105%28%28-+a%5B1%5D%29%2F2%29 ALIGN=MIDDLE  ALT=\"-+300+=+15a%5B1%5D+%2B+105%28%28-+a%5B1%5D%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+a%5B1%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28-+a%5B1%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for d in eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+300+=+15a%5B1%5D+%2B+52.5%28-+a%5B1%5D%29 ALIGN=MIDDLE  ALT=\"-+300+=+15a%5B1%5D+%2B+52.5%28-+a%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+300+=+15a%5B1%5D+-+52.5a%5B1%5D ALIGN=MIDDLE  ALT=\"-+300+=+15a%5B1%5D+-+52.5a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+37.5a%5B1%5D+=+-+300 ALIGN=MIDDLE  ALT=\"-+37.5a%5B1%5D+=+-+300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 1st term = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+300%29%2F-+37.5 ALIGN=MIDDLE  ALT=\"%28-+300%29%2F-+37.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%288%29 ALIGN=MIDDLE  ALT=\"highlight_green%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can do the check!!\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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