document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995635>Question 995635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to use one of the arithmetic series formula. The arithmetic series 5 + 9 + 13 +...+ tn has a sum of 945. How many terms does this series have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614956 by </B><A HREF=/tutors/aboutme.mpl?userid=atique.ah><B>atique.ah(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=atique.ah><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=614956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sn=(t1+tn)*(n/2)<BR>\n" );
document.write( "945=(5+tn)*(n/2)<BR>\n" );
document.write( "945*2=(5+tn)*n<BR>\n" );
document.write( "1890=(5+tn)*n  .......... 1\r<BR>\n" );
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document.write( "tn=t1+(n-1)d<BR>\n" );
document.write( "tn=5+(n-1)4<BR>\n" );
document.write( "tn=5+4n-4<BR>\n" );
document.write( "tn=1+4n  ................2\r<BR>\n" );
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document.write( "substituting the value of tn in eq 1<BR>\n" );
document.write( "1890=(5+1+4n)*n<BR>\n" );
document.write( "1890=(6+4n)*n<BR>\n" );
document.write( "1890=6n+4n^2 or writing in the standard form<BR>\n" );
document.write( "4n^2+6n-1890=0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=an%5E2%2Bbn%2Bc=0 ALIGN=MIDDLE  ALT=\"an%5E2%2Bbn%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B3n%2B-945+=+0 ALIGN=MIDDLE  ALT=\"2n%5E2%2B3n%2B-945+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"n%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A2%2A-945=7569 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A2%2A-945=7569\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=7569 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+7569+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+7569+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D+=+%28-%283%29%2Bsqrt%28+7569+%29%29%2F2%5C2+=+21 ALIGN=MIDDLE  ALT=\"n%5B1%5D+=+%28-%283%29%2Bsqrt%28+7569+%29%29%2F2%5C2+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D+=+%28-%283%29-sqrt%28+7569+%29%29%2F2%5C2+=+-22.5 ALIGN=MIDDLE  ALT=\"n%5B2%5D+=+%28-%283%29-sqrt%28+7569+%29%29%2F2%5C2+=+-22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B3n%2B-945 ALIGN=MIDDLE  ALT=\"2n%5E2%2B3n%2B-945\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B3n%2B-945+=+2%28n-21%29%2A%28n--22.5%29 ALIGN=MIDDLE  ALT=\"2n%5E2%2B3n%2B-945+=+2%28n-21%29%2A%28n--22.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 21, -22.5.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-945+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-945+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The series have 21 terms because n cannot be a fraction </SPAN>\n" );
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