document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217318>Question 217318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The third term of an arithmetic sequence is 4 and the sum of the first 8 term is 36. Write down the first 8 term 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 #163891 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The third term of an arithmetic sequence is 4 and the sum of the first 8 term is 36. Write down the first 8 term of the sequence. \r<BR>\n" );
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document.write( "Step 1.  An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value \r<BR>\n" );
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document.write( "Step 2.  Let x be the number to add or subtract in the sequence.\r<BR>\n" );
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document.write( "Step 3.  Let a be the first term, let a+x be the second term, let a+2x be the third term, a+3x be the fourth term, and a+(n-1)x be the nth term\r<BR>\n" );
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document.write( "Step 4.  Let a+7x be the 8th term.   Then the sum of the first and eighth term is a+a+7x=2a+7x.  The sum of the second term and seventh term is the a+x+a+6x=2a+6x.  So four the first eight terms, there will be four pairs of 2a+6x which will equal to 36 or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%282a%2B7x%29=36 ALIGN=MIDDLE  ALT=\"4%2A%282a%2B7x%29=36\"   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=2a%2B7x=9 ALIGN=MIDDLE  ALT=\"2a%2B7x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A\r<BR>\n" );
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document.write( "Also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2x=4 ALIGN=MIDDLE  ALT=\"a%2B2x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation B since the 3th term is 4.\r<BR>\n" );
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document.write( "Step 5.  Then we have a system of equations given as Equations A and B.  The following steps will solve the equation by substitution.\r<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++++2%5Ca+%2B+7%5Cx+=+9%2C%0D%0A++++1%5Ca+%2B+2%5Cx+=+4+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Ca+%2B+7%5Cx+=+9%2C%0D%0A++++1%5Ca+%2B+2%5Cx+=+4+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 7*x to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa+=+9+-+7%2Ax ALIGN=MIDDLE  ALT=\"2%2Aa+=+9+-+7%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+9%2F2+-+7%2Ax%2F2 ALIGN=MIDDLE  ALT=\"a+=+9%2F2+-+7%2Ax%2F2\"   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=1%2A%289%2F2+-+7%2Ax%2F2%29+%2B+2%5Cx+=+4 ALIGN=MIDDLE  ALT=\"1%2A%289%2F2+-+7%2Ax%2F2%29+%2B+2%5Cx+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that x=0.333333333333333. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+9%2F2+-+7%2Ax%2F2 ALIGN=MIDDLE  ALT=\"a+=+9%2F2+-+7%2Ax%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a=3.33333333333333.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+a=3.33333333333333%2C+x=0.333333333333333+%29 ALIGN=MIDDLE  ALT=\"system%28+a=3.33333333333333%2C+x=0.333333333333333+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and x=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So sequence is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F3 ALIGN=MIDDLE  ALT=\"11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F3 ALIGN=MIDDLE  ALT=\"13%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F3 ALIGN=MIDDLE  ALT=\"14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F3 ALIGN=MIDDLE  ALT=\"17%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Check:  The third term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2B11%2B12%2B13%2B14%2B15%2B16%2B17%29%2F3=36 ALIGN=MIDDLE  ALT=\"%2810%2B11%2B12%2B13%2B14%2B15%2B16%2B17%29%2F3=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Step 6.   ANSWER:  The sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3 ALIGN=MIDDLE  ALT=\"10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F3 ALIGN=MIDDLE  ALT=\"11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F3 ALIGN=MIDDLE  ALT=\"13%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F3 ALIGN=MIDDLE  ALT=\"14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F3 ALIGN=MIDDLE  ALT=\"17%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I hope the above steps and explanation were helpful. \r<BR>\n" );
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document.write( "For Step-By-Step videos on Introduction to Algebra, \r<BR>\n" );
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document.write( "please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and \r<BR>\n" );
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document.write( "for Trigonometry please visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/Trigonometry. \r<BR>\n" );
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document.write( "Also, good luck in your studies and contact me at \r<BR>\n" );
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document.write( "john@e-liteworks.com for your future math needs.\r<BR>\n" );
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document.write( "Respectfully, <BR>\n" );
document.write( "Dr J\r<BR>\n" );
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