document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083553>Question 1083553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The arithmetic progression consists of 15 terms. If the sum of the 3 terms<BR>\n" );
document.write( "in the middle is 27 and the sum of the last 3 terms is 18, then what is the <BR>\n" );
document.write( "sum of the first 3 terms? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697643 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The arithmetic progression consists of 15 terms. If the sum of the 3 terms<BR>\n" );
document.write( "in the middle is 27 and the sum <BR>\n" );
document.write( "of the last 3 terms is 18, then what is the sum of the first 3 terms?<BR>\n" );
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document.write( "\"If the sum of the 3 terms in the middle is 27\" then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B8%5D ALIGN=MIDDLE  ALT=\"a%5B8%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2F3 ALIGN=MIDDLE  ALT=\"27%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9  (why ?)\r\n" );
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document.write( "Also, \"if the sum of the last 3 terms is 18\" then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B14%5D ALIGN=MIDDLE  ALT=\"a%5B14%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F3 ALIGN=MIDDLE  ALT=\"18%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.\r\n" );
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document.write( "Thus you have \r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B8%5D ALIGN=MIDDLE  ALT=\"a%5B8%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B7%2Ad ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B7%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9     (1)   and\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B14%5D ALIGN=MIDDLE  ALT=\"a%5B14%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B13%2Ad ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B13%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6   (2) \r\n" );
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document.write( "It implies that 6d = 6 - 9 = -3.   Hence,  d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F6 ALIGN=MIDDLE  ALT=\"%28-3%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -0.5.\r\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B8%5D-6d ALIGN=MIDDLE  ALT=\"a%5B8%5D-6d\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9 - 6*(-0.5) = 9 + 3 = 12.\r\n" );
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document.write( "Hence, the sum  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 36    (why ?)\r\n" );
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document.write( "<U>Answer</U>.  36.\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "There is a bunch of lessons on arithmetic progressions in this site:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-and-arithmetic-progressions.lesson>Mathematical induction and arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-arithmetic-progressions.lesson>Solved problems on arithmetic progressions</A> \r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic <U>\"Arithmetic progressions\"</U>.\r<BR>\n" );
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