document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937656>Question 937656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given an arithmetic sequence with total of the first three terms is equal to 13 and the last N th term is equal to 7. Determine the middle term of arithmetic sequence and its value  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571078 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=571078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Any term at index i would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D%2B%28i-1%29d ALIGN=MIDDLE  ALT=\"A%5B1%5D%2B%28i-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for common difference of d.\r<BR>\n" );
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document.write( "Your description with the last N th term must mean, index of 3 because your sequence is given to have three terms.\r<BR>\n" );
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document.write( "To be simple, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=A%5B1%5D ALIGN=MIDDLE  ALT=\"a=A%5B1%5D\"   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=a%2B%281-1%29d%2Ba%2B%282-1%29d%2Ba%2B%283-1%29d=13 ALIGN=MIDDLE  ALT=\"a%2B%281-1%29d%2Ba%2B%282-1%29d%2Ba%2B%283-1%29d=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ba%2Bd%2Ba%2B2d=13 ALIGN=MIDDLE  ALT=\"a%2Ba%2Bd%2Ba%2B2d=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283a%2B3d=13%29 ALIGN=MIDDLE  ALT=\"highlight_green%283a%2B3d=13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One equation in two unknowns.\r<BR>\n" );
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document.write( "More from the description,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B%283-1%29d=7 ALIGN=MIDDLE  ALT=\"a%2B%283-1%29d=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%2B2d=7%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%2B2d=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we have two equation in the two unknowns, a and d.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283a%2B3d=13%2Ca%2B2d=7%29 ALIGN=MIDDLE  ALT=\"system%283a%2B3d=13%2Ca%2B2d=7%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%283a%2B3d=13%2C3a%2B6d=21%29 ALIGN=MIDDLE  ALT=\"system%283a%2B3d=13%2C3a%2B6d=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, starting with Elimination Method<BR>\n" );
document.write( "E2-E1 gives.....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3d=8 ALIGN=MIDDLE  ALT=\"3d=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=8%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28d=8%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The middle, or term at index 2, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8%2F3=21%2F3-8%2F3=highlight%2813%2F3%29 ALIGN=MIDDLE  ALT=\"7-8%2F3=21%2F3-8%2F3=highlight%2813%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "....Only three terms are in the sequence.  <BR>\n" );
document.write( "\"...sequence with total of the first three terms is equal to 13...\"<BR>\n" );
document.write( "and <BR>\n" );
document.write( "\" last N th term is equal to 7.\"<BR>\n" );
document.write( "and<BR>\n" );
document.write( "\"Determine the middle term of arithmetic sequence\".<BR>\n" );
document.write( "Those strongly imply that the last term of the sequence is at index number 3. </SPAN>\n" );
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