document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933569>Question 933569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> we have to arrange chairs for the audience a in the first row we can place 20 chairs in the next 22 chairs 2 chairs can be added to each row than the previous one we have to arrange 50 so how many chairs are needed WE HAVE TO USE AP FORMULA <BR>\n" );
document.write( "                              (arithmetic progression)\r<BR>\n" );
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document.write( "so how many chairs will be in the 25th row?\r<BR>\n" );
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document.write( "with thousand how many perfect rows can you make? \r<BR>\n" );
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document.write( "how many chairs will be in the last row? \r<BR>\n" );
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document.write( "what are the difference in the number of chairs for arranging 25 rows and 50 rows? \r<BR>\n" );
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document.write( "in which row 50 chairs will exist? \r<BR>\n" );
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document.write( "will you be able to make perfect rows with thousand chairs? if not how many chairs are needed to make the row perfect?\r<BR>\n" );
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document.write( "if you need to make 2 more rows how more chairs are needed?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566916 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=566916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # of chairs in rows: 20, 22,24,26,28,30,32,34,36,38,40,42,44,46,48,50\r<BR>\n" );
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document.write( "difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2 ALIGN=MIDDLE  ALT=\"d=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=20 ALIGN=MIDDLE  ALT=\"a%5B1%5D=20\"   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%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a.<BR>\n" );
document.write( " how many chairs will be in the 25th row?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B25+%5D=+20+%2B+%2825-1%292 ALIGN=MIDDLE  ALT=\"a%5B25+%5D=+20+%2B+%2825-1%292\"   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%5B25+%5D=20%2B50-2 ALIGN=MIDDLE  ALT=\"+a%5B25+%5D=20%2B50-2\"   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=a%5B25+%5D=68 ALIGN=MIDDLE  ALT=\"a%5B25+%5D=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >...chairs will be in the 25th row\r<BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > chairs  how many perfect rows can you make\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=+20+%2B+%28n-1%292 ALIGN=MIDDLE  ALT=\"1000=+20+%2B+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000-20+=+%28n-1%292 ALIGN=MIDDLE  ALT=\"1000-20+=+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=980+=+%28n-1%292 ALIGN=MIDDLE  ALT=\"980+=+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=980+%2F2=+%28n-1%29 ALIGN=MIDDLE  ALT=\"980+%2F2=+%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=490=+n+-1 ALIGN=MIDDLE  ALT=\"490=+n+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=491=+n ALIGN=MIDDLE  ALT=\"491=+n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....# of  rows  you can make, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=491 ALIGN=MIDDLE  ALT=\"491\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a perfect number, \r<BR>\n" );
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document.write( "the only perfect numbers between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=496 ALIGN=MIDDLE  ALT=\"496\"   DISABLED_style= \"max-width:90%; height:auto;\" >; since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=496%3E491 ALIGN=MIDDLE  ALT=\"496%3E491\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,  with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > chairs  you can  make only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > perfect rows which are rows <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.\r<BR>\n" );
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document.write( "how many chairs will be in the last row? <BR>\n" );
document.write( " the last row is <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;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn+%5D=+20+%2B+%28n-1%292 ALIGN=MIDDLE  ALT=\"a%5Bn+%5D=+20+%2B+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...# chairs in the last row\r<BR>\n" );
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document.write( "d.\r<BR>\n" );
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document.write( "what are the difference in the number of chairs for arranging 25 rows and 50 rows? <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B25+%5D=68 ALIGN=MIDDLE  ALT=\"a%5B25+%5D=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >...chairs will be in the 25th row\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B50+%5D=+20+%2B+%2850-1%292 ALIGN=MIDDLE  ALT=\"a%5B50+%5D=+20+%2B+%2850-1%292\"   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%5B50+%5D=+20+%2B+%2849%292 ALIGN=MIDDLE  ALT=\"a%5B50+%5D=+20+%2B+%2849%292\"   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%5B50+%5D=+20+%2B+98 ALIGN=MIDDLE  ALT=\"a%5B50+%5D=+20+%2B+98\"   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%5B50+%5D=+118 ALIGN=MIDDLE  ALT=\"a%5B50+%5D=+118\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the difference in the number of chairs for arranging <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > rows and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > rows is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=118-68=50 ALIGN=MIDDLE  ALT=\"118-68=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or, since  the difference in the number of chairs for arranging between two rows  is 2 chairs, then<BR>\n" );
document.write( "between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > rows and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2A2=50 ALIGN=MIDDLE  ALT=\"25%2A2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e.<BR>\n" );
document.write( "in which row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > chairs will exist? \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50+=+20+%2B+%28n-1%292 ALIGN=MIDDLE  ALT=\"50+=+20+%2B+%28n-1%292\"   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=50+-+20+=+%28n-1%292 ALIGN=MIDDLE  ALT=\"50+-+20+=+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F2+=+%28n-1%29 ALIGN=MIDDLE  ALT=\"30%2F2+=+%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B1=+n ALIGN=MIDDLE  ALT=\"15%2B1=+n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=16 ALIGN=MIDDLE  ALT=\"n=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....row in which  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > chairs will exist\r<BR>\n" );
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document.write( "f.<BR>\n" );
document.write( "will you be able to make perfect rows with thousand chairs? if not how many chairs are needed to make the row perfect? \r<BR>\n" );
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document.write( "from c. we know that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B491+%5D=1000+ ALIGN=MIDDLE  ALT=\"a%5B491+%5D=1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=491 ALIGN=MIDDLE  ALT=\"491\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not  perfect row because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=491 ALIGN=MIDDLE  ALT=\"491\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a perfect number<BR>\n" );
document.write( "first perfect number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=496 ALIGN=MIDDLE  ALT=\"n=496\"   DISABLED_style= \"max-width:90%; height:auto;\" >(see b.); so we need 5more rows or 10 more chairs<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B496%5D=+20+%2B+%28496-1%292 ALIGN=MIDDLE  ALT=\"a%5B496%5D=+20+%2B+%28496-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B496%5D=20+%2B%28495%292 ALIGN=MIDDLE  ALT=\"a%5B496%5D=20+%2B%28495%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B496+%5D-100=20%2B990 ALIGN=MIDDLE  ALT=\"a%5B496+%5D-100=20%2B990\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B496+%5D=1010 ALIGN=MIDDLE  ALT=\"a%5B496+%5D=1010\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "g.\r<BR>\n" );
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document.write( "if you need to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > more rows you will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=498 ALIGN=MIDDLE  ALT=\"498\"   DISABLED_style= \"max-width:90%; height:auto;\" > rows\r<BR>\n" );
document.write( "\n" );
document.write( "as given,for each additional row you need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > more chair; so,  to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > more rows  you will need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > more chairs to row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=496 ALIGN=MIDDLE  ALT=\"496\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1010 ALIGN=MIDDLE  ALT=\"1010\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, we will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1014 ALIGN=MIDDLE  ALT=\"1014\"   DISABLED_style= \"max-width:90%; height:auto;\" >  chairs in row # <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=498 ALIGN=MIDDLE  ALT=\"498\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1014=+20+%2B+%28n-1%292 ALIGN=MIDDLE  ALT=\"1014=+20+%2B+%28n-1%292\"   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=1014=+20+%2B+%28n-1%292 ALIGN=MIDDLE  ALT=\"1014=+20+%2B+%28n-1%292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1014-20+=2n-2+ ALIGN=MIDDLE  ALT=\"1014-20+=2n-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=994%2B2=2n ALIGN=MIDDLE  ALT=\"994%2B2=2n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=996=2n ALIGN=MIDDLE  ALT=\"996=2n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=996%2F2=n ALIGN=MIDDLE  ALT=\"996%2F2=n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=498 ALIGN=MIDDLE  ALT=\"n=498\"   DISABLED_style= \"max-width:90%; height:auto;\" >...so, we got a row number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=498 ALIGN=MIDDLE  ALT=\"498\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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