document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=743400>Question 743400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of all terms of the arithmetic progression having      ten terms except for the first term is 99 and except for   the sixth term 89. Find the third term of the progression      if the sum of the first term and the fifth term is equal to 10. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452870 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=452870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= first term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common difference<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" >= sum of all 10 terms<BR>\n" );
document.write( " <BR>\n" );
document.write( "The sum of all terms of the arithmetic progression except for the first term is 99 translates into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S-a%5B1%5D=99 ALIGN=MIDDLE  ALT=\"S-a%5B1%5D=99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of all terms of the arithmetic progression except for the sixth term 89 translates into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S-a%5B6%5D=99 ALIGN=MIDDLE  ALT=\"S-a%5B6%5D=99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28S-a%5B1%5D=99%2CS-a%5B6%5D=89%29 ALIGN=MIDDLE  ALT=\"system%28S-a%5B1%5D=99%2CS-a%5B6%5D=89%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D-a%5B1%5D=99-89 ALIGN=MIDDLE  ALT=\"a%5B6%5D-a%5B1%5D=99-89\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D-a%5B1%5D=10 ALIGN=MIDDLE  ALT=\"a%5B6%5D-a%5B1%5D=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The nth term in an arithmetic progression is given by the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=a%5B1%5D%2B5d ALIGN=MIDDLE  ALT=\"a%5B6%5D=a%5B1%5D%2B5d\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D-a%5B1%5D=5d ALIGN=MIDDLE  ALT=\"a%5B6%5D-a%5B1%5D=5d\"   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=system%28a%5B6%5D-a%5B1%5D=10%2Ca%5B6%5D-a%5B1%5D=5d%29 ALIGN=MIDDLE  ALT=\"system%28a%5B6%5D-a%5B1%5D=10%2Ca%5B6%5D-a%5B1%5D=5d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5d=10 ALIGN=MIDDLE  ALT=\"5d=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <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( " <BR>\n" );
document.write( "We are told that the sum of the first term and the fifth term is equal to 10.<BR>\n" );
document.write( "The fifth term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D%2B%285-1%29%2A2 ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D%2B%285-1%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D%2B8 ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of the first term and the fifth term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B%28a%5B1%5D%2B8%29=10 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B%28a%5B1%5D%2B8%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5B1%5D%2B8=10 ALIGN=MIDDLE  ALT=\"2a%5B1%5D%2B8=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5B1%5D=10-8 ALIGN=MIDDLE  ALT=\"2a%5B1%5D=10-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5B1%5D=2 ALIGN=MIDDLE  ALT=\"2a%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <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;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Knowing that the first term is <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;\" > and the common difference is <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;\" > we can calculate the third term as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=1%2B%283-1%29%2A2 ALIGN=MIDDLE  ALT=\"a%5B3%5D=1%2B%283-1%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=1%2B2%2A2 ALIGN=MIDDLE  ALT=\"a%5B3%5D=1%2B2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=1%2B4 ALIGN=MIDDLE  ALT=\"a%5B3%5D=1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B3%5D=5%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B3%5D=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );