document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662463>Question 662463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: The arithmetic series 5 + 9 + 13 + ... + tn has a sum of 945. How many terms does the series have?\r<BR>\n" );
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document.write( "I was just having an issue trying to figure out what formula to use. Any help would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412290 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum s of an arithmetic series with first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms, and common difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+n%28+2a+%2B+%28n+-+1%29d+%29+%2F+2 ALIGN=MIDDLE  ALT=\"s+=+n%28+2a+%2B+%28n+-+1%29d+%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Applying this to the given series:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=945+=+n%28+2+%2A+5+%2B+4%28n+-+1%29+%29+%2F+2 ALIGN=MIDDLE  ALT=\"945+=+n%28+2+%2A+5+%2B+4%28n+-+1%29+%29+%2F+2\"   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=945+=+n%28+10+%2B+4n+-+4+%29+%2F+2 ALIGN=MIDDLE  ALT=\"945+=+n%28+10+%2B+4n+-+4+%29+%2F+2\"   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=945+=+2n%28+4n+%2B6+%29+%2F+2 ALIGN=MIDDLE  ALT=\"945+=+2n%28+4n+%2B6+%29+%2F+2\"   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=945+=+2n%28+2n+%2B3+%29+%2F+2 ALIGN=MIDDLE  ALT=\"945+=+2n%28+2n+%2B3+%29+%2F+2\"   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=945+=+cross%282%29n%28+2n+%2B3+%29+%2Fcross%28+2%29 ALIGN=MIDDLE  ALT=\"945+=+cross%282%29n%28+2n+%2B3+%29+%2Fcross%28+2%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=945+=+n%28+2n+%2B3+%29+ ALIGN=MIDDLE  ALT=\"945+=+n%28+2n+%2B3+%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=945+=+2n%5E2+%2B3n++ ALIGN=MIDDLE  ALT=\"945+=+2n%5E2+%2B3n++\"   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=2n%5E2+%2B+3n+-+945+=+0 ALIGN=MIDDLE  ALT=\"2n%5E2+%2B+3n+-+945+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor...replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n ALIGN=MIDDLE  ALT=\"3n\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-42n%2B+45n ALIGN=MIDDLE  ALT=\"-42n%2B+45n\"   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=2n%5E2+-42n%2B+45n+-+945+=+0 ALIGN=MIDDLE  ALT=\"2n%5E2+-42n%2B+45n+-+945+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n%5E2+-42n%29%2B+%2845n+-+945%29+=+0 ALIGN=MIDDLE  ALT=\"%282n%5E2+-42n%29%2B+%2845n+-+945%29+=+0\"   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=2n%28n+-21%29%2B+45%28n+-+21%29+=+0 ALIGN=MIDDLE  ALT=\"2n%28n+-21%29%2B+45%28n+-+21%29+=+0\"   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=%282n+%2B+45%29%28n+-+21%29+=+0 ALIGN=MIDDLE  ALT=\"%282n+%2B+45%29%28n+-+21%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The positive root <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+21 ALIGN=MIDDLE  ALT=\"n+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number ALIGN=MIDDLE  ALT=\"number\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=terms ALIGN=MIDDLE  ALT=\"terms\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "so, your sequence is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29 ALIGN=MIDDLE  ALT=\"29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33 ALIGN=MIDDLE  ALT=\"33\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37 ALIGN=MIDDLE  ALT=\"37\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41 ALIGN=MIDDLE  ALT=\"41\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53 ALIGN=MIDDLE  ALT=\"53\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57 ALIGN=MIDDLE  ALT=\"57\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61 ALIGN=MIDDLE  ALT=\"61\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69 ALIGN=MIDDLE  ALT=\"69\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73 ALIGN=MIDDLE  ALT=\"73\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77 ALIGN=MIDDLE  ALT=\"77\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85 ALIGN=MIDDLE  ALT=\"85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the sum is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B9%2B13%2B17%2B21%2B25%2B29%2B33%2B37%2B41%2B45%2B49%2B53%2B57%2B61%2B64%2B69%2B73%2B77%2B81%2B85+=+945 ALIGN=MIDDLE   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=945+=+945 ALIGN=MIDDLE  ALT=\"945+=+945\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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