document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983043>Question 983043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the first and the last terms of a linear sequence (A.P) is 42. if the sum of all the terms is 420 and the second the is 4 . find the the number of terms,the common difference and the last 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 #603855 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=603855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This solution is not finished.\r<BR>\n" );
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document.write( "Using expression for general term of the sequence, A for first term, when n=1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"A%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "The description will give this system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A%2BA%2B%28n-1%29d=42%2C%28n%2F2%29%28A%2BA%2B%28n-1%29d%29=420%2CA%2Bd=4%29 ALIGN=MIDDLE  ALT=\"system%28A%2BA%2B%28n-1%29d=42%2C%28n%2F2%29%28A%2BA%2B%28n-1%29d%29=420%2CA%2Bd=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Some simplification,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282A%2Bnd-d=42%2C%28n%2F2%29%282A%2Bnd-d%29=420%2CA%2Bd=4%29 ALIGN=MIDDLE  ALT=\"system%282A%2Bnd-d=42%2C%28n%2F2%29%282A%2Bnd-d%29=420%2CA%2Bd=4%29\"   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=system%282A%2Bnd-d=42%2Cn%282A%2Bnd-d%29=840%2Cd=4-A%29 ALIGN=MIDDLE  ALT=\"system%282A%2Bnd-d=42%2Cn%282A%2Bnd-d%29=840%2Cd=4-A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Try substituting for d in the first two equations of this last form of the system....\r<BR>\n" );
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document.write( "...  Working through the algebra steps for that brings to the system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283A%2B4n-nA-4=42%2Cn%283A%2B4n-nA-4%29=840%29 ALIGN=MIDDLE  ALT=\"system%283A%2B4n-nA-4=42%2Cn%283A%2B4n-nA-4%29=840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dividing the second equation by the first equation gives<BR>\n" );
document.write( "(because notice the four-term polynomial expression in both equations)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=840%2F42 ALIGN=MIDDLE  ALT=\"n=840%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=20%29 ALIGN=MIDDLE  ALT=\"highlight%28n=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Review everything and try to understand, and then continue to find A and d. </SPAN>\n" );
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