document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831708>Question 831708</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The 11th term of an arthmetric sequence is 57 and the sum of the first and fourth terms is 29. Determine the first 3 terms of the sequence<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501602 by </B><A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><B>hovuquocan1997(83)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><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=501602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a formula to find any term in a arithmetic sequence and it is<BR>\n" );
document.write( "Term = a + d(n - 1) <BR>\n" );
document.write( "in which a is the first term and d is the difference between the terms, and n is the number of the term<BR>\n" );
document.write( "ok so we have 11th term is 57, the equation will be<BR>\n" );
document.write( "57 = a + d(11-1)<BR>\n" );
document.write( "a + 10d = 57<BR>\n" );
document.write( "That's the first equation<BR>\n" );
document.write( "Now we move to the second one<BR>\n" );
document.write( "We have First term is just \"a\"<BR>\n" );
document.write( "and fourth term is a+d(4-1) = a + 3d<BR>\n" );
document.write( "We have the sum of first and fourth terms is 29, that means a + a + 3d = 29<BR>\n" );
document.write( "2a + 3d = 29 <BR>\n" );
document.write( "That's the second equation, now we have a system of 2 equations to solve for a, d<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Ca+%2B+10%5Cd+=+57%2C%0D%0A++++2%5Ca+%2B+3%5Cd+=+29+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Ca+%2B+10%5Cd+=+57%2C%0D%0A++++2%5Ca+%2B+3%5Cd+=+29+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 10*d to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Aa+=+57+-+10%2Ad ALIGN=MIDDLE  ALT=\"1%2Aa+=+57+-+10%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+57%2F1+-+10%2Ad%2F1 ALIGN=MIDDLE  ALT=\"a+=+57%2F1+-+10%2Ad%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%2857%2F1+-+10%2Ad%2F1%29+%2B+3%5Cd+=+29 ALIGN=MIDDLE  ALT=\"2%2A%2857%2F1+-+10%2Ad%2F1%29+%2B+3%5Cd+=+29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that d=5. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+57%2F1+-+10%2Ad%2F1 ALIGN=MIDDLE  ALT=\"a+=+57%2F1+-+10%2Ad%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a=7.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+a=7%2C+d=5+%29 ALIGN=MIDDLE  ALT=\"system%28+a=7%2C+d=5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Now you know that a = 7, meaning that the first term is 7 <BR>\n" );
document.write( "d is 5, so the second term is 12, and the third term is 17<BR>\n" );
document.write( "So the answer is 7, 12, 17<BR>\n" );
document.write( "TA-DAH<BR>\n" );
document.write( ":D  </SPAN>\n" );
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