document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=336261>Question 336261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of an arithmetic series is 1356 and the first term is -1. If the common difference is 5, how many terms are in the sequence? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #241090 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=241090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> arithmetic series:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+%2B+%28a%5B1%5D%2Bdiff%29%2B%28a%5B1%5D%2B2%2Adiff%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D+%2B+%28a%5B1%5D%2Bdiff%29%2B%28a%5B1%5D%2B2%2Adiff%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > +...+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2B%28n-1%29%2Adiff%29=sum%28%28a%5B1%5D%2B%28i-1%29%2Adiff%29%29%29 ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2B%28n-1%29%2Adiff%29=sum%28%28a%5B1%5D%2B%28i-1%29%2Adiff%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > summed from i=1 to n<BR>\n" );
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document.write( "Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, diff=5 and sum=1356<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28a%5B1%5D%2B%28i-1%29%2Adiff%29%29=sum%28%28-1%2B%28i-1%29%2A5%29%29=1356 ALIGN=MIDDLE  ALT=\"sum%28%28a%5B1%5D%2B%28i-1%29%2Adiff%29%29=sum%28%28-1%2B%28i-1%29%2A5%29%29=1356\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%285i-6%29%29=1356 ALIGN=MIDDLE  ALT=\"sum%28%285i-6%29%29=1356\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asum%28i%29-n%2A6=1356 ALIGN=MIDDLE  ALT=\"5%2Asum%28i%29-n%2A6=1356\"   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=5%2An%2A%28n%2B1%29%2F2-6%2An=1356 ALIGN=MIDDLE  ALT=\"5%2An%2A%28n%2B1%29%2F2-6%2An=1356\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2An%2A%28n-1%29-12%2An=2712 ALIGN=MIDDLE  ALT=\"5%2An%2A%28n-1%29-12%2An=2712\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (multiply both sides by 2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%2B5%2An-12%2An=2712 ALIGN=MIDDLE  ALT=\"5n%5E2%2B5%2An-12%2An=2712\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2An%5E2-7%2An-2712=0 ALIGN=MIDDLE  ALT=\"5%2An%5E2-7%2An-2712=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "using quadratic solution<BR>\n" );
document.write( "with a=5, b=-7, c=-2712<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%287-Sqrt%287%5E2-4%2A%285%29%2A%28-2712%29%29%29%2F%282%2A5%29=%287-233%29%2F10=-22.6 ALIGN=MIDDLE  ALT=\"n=%287-Sqrt%287%5E2-4%2A%285%29%2A%28-2712%29%29%29%2F%282%2A5%29=%287-233%29%2F10=-22.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%287%2BSqrt%287%5E2-4%2A%285%29%2A%28-2712%29%29%29%2F%282%2A5%29=%287%2B233%29%2F10=24 ALIGN=MIDDLE  ALT=\"n=%287%2BSqrt%287%5E2-4%2A%285%29%2A%28-2712%29%29%29%2F%282%2A5%29=%287%2B233%29%2F10=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "since we need the solution to be positive, the first solution is not needed<BR>\n" );
document.write( "and n=24\r<BR>\n" );
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