document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979025>Question 979025</A>: <I><SPAN STYLE=\"word-break: break-all;\">              1<BR>\n" );
document.write( "           2  3<BR>\n" );
document.write( "         4  5  6<BR>\n" );
document.write( "       7  8  9  10<BR>\n" );
document.write( "    11 12 13 14 15<BR>\n" );
document.write( ".... .... .... .... .... .....<BR>\n" );
document.write( " a) what's the 3rd number from left in 10th row?<BR>\n" );
document.write( " b) what's the position of 2009? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600465 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each row has one more number than the row above.<BR>\n" );
document.write( "It is what math teachers call an arithmetic sequence, or an arithmetic progression.<BR>\n" );
document.write( "(It depends on where you go to school).<BR>\n" );
document.write( "Row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=n ALIGN=MIDDLE  ALT=\"a%5Bn%5D=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers,<BR>\n" );
document.write( "and rows <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > contain a total of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=sum%28a%5Bi%5D%2Ci=1%2Cn%29=n%28n%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=sum%28a%5Bi%5D%2Ci=1%2Cn%29=n%28n%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers.<BR>\n" );
document.write( "That means that the last number on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=n%28n%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=n%28n%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "The last number on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B9%5D=9%2A10%2F2=45 ALIGN=MIDDLE  ALT=\"S%5B9%5D=9%2A10%2F2=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the third number in row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2B3=highlight%2848%29 ALIGN=MIDDLE  ALT=\"45%2B3=highlight%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "If we say that number 2009 is in row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the last number on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%2F2%3C2009 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%2F2%3C2009\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%2F2%3C2009 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%2F2%3C2009\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2%2Bn%29%2F2%3C2009 ALIGN=MIDDLE  ALT=\"%28n%5E2%2Bn%29%2F2%3C2009\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn%3C2%2A2009 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn%3C2%2A2009\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn%3C4018 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn%3C4018\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is more than one way to solve that inequality.<BR>\n" );
document.write( "You could find the solutions to the quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn=4018 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn=4018\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn-4018=0 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn-4018=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%28-1+%2B-+sqrt%2816073%29%29%2F2 ALIGN=MIDDLE  ALT=\"n=%28-1+%2B-+sqrt%2816073%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and realize that the solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn%3C4018 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn%3C4018\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn-4018%3C0 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn-4018%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3C%28-1%2Bsqrt%2816073%29%29%2F2=about+62.9 ALIGN=MIDDLE  ALT=\"n%3C%28-1%2Bsqrt%2816073%29%29%2F2=about+62.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=62 ALIGN=MIDDLE  ALT=\"n=62\"   DISABLED_style= \"max-width:90%; height:auto;\" > marks the row above number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2009 ALIGN=MIDDLE  ALT=\"2009\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The last number on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=62 ALIGN=MIDDLE  ALT=\"n=62\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B62%5D=62%2A63%2F2=1953 ALIGN=MIDDLE  ALT=\"S%5B62%5D=62%2A63%2F2=1953\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and you need to go <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2009-1953=56 ALIGN=MIDDLE  ALT=\"2009-1953=56\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers further,<BR>\n" );
document.write( "on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=62%2B1=63 ALIGN=MIDDLE  ALT=\"n%2B1=62%2B1=63\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2009 ALIGN=MIDDLE  ALT=\"2009\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2009 ALIGN=MIDDLE  ALT=\"2009\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2856th%29 ALIGN=MIDDLE  ALT=\"highlight%2856th%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > number on row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2863%29 ALIGN=MIDDLE  ALT=\"highlight%2863%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );