document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=845973>Question 845973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ninth term of an arithmeticsequence is 42 and the sum of the fist term is 414. Find the first term of the sequence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509548 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the first term of the AP be 'a' and the common difference be 'd'.<BR>\n" );
document.write( "Therefore the n-th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D=a%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D=a%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum up to first n-terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=n%282a%2B%28n-1%29d%29%2F2 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=n%282a%2B%28n-1%29d%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, n=9, \r<BR>\n" );
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document.write( "9th term is given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B9%5D=42 ALIGN=MIDDLE  ALT=\"t%5B9%5D=42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B%289-1%29d+=+42 ALIGN=MIDDLE  ALT=\"a%2B%289-1%29d+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B8d=42 ALIGN=MIDDLE  ALT=\"a%2B8d=42\"   DISABLED_style= \"max-width:90%; height:auto;\" > _______ (1)\r<BR>\n" );
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document.write( "Sum of first 9 terms is given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B9%5D=414 ALIGN=MIDDLE  ALT=\"S%5B9%5D=414\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%282a%2B%289-1%29d%29%2F2=414 ALIGN=MIDDLE  ALT=\"9%282a%2B%289-1%29d%29%2F2=414\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%282a%2B8d%29%2F2=414 ALIGN=MIDDLE  ALT=\"9%282a%2B8d%29%2F2=414\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28a%2B4d%29=414 ALIGN=MIDDLE  ALT=\"9%28a%2B4d%29=414\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4d=414%2F9 ALIGN=MIDDLE  ALT=\"a%2B4d=414%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4d=46 ALIGN=MIDDLE  ALT=\"a%2B4d=46\"   DISABLED_style= \"max-width:90%; height:auto;\" > _______ (2)\r<BR>\n" );
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document.write( "Subtracting both sides of equation (2) from (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4d=-4 ALIGN=MIDDLE  ALT=\"4d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-1 ALIGN=MIDDLE  ALT=\"d=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-1 ALIGN=MIDDLE  ALT=\"d=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (2) we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-4=46 ALIGN=MIDDLE  ALT=\"a-4=46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=50 ALIGN=MIDDLE  ALT=\"a=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First term of the sequence is 50.\r<BR>\n" );
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document.write( "Cheers!!! </SPAN>\n" );
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