document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094753>Question 1094753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The six term of an arithmetic progression is 23 and the sum of the first six terms is 78.Find<BR>\n" );
document.write( "(a)the common difference and the first term<BR>\n" );
document.write( "(b)the tenth term </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709325 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=709325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28cross%28six%29%29 ALIGN=MIDDLE  ALT=\"highlight%28cross%28six%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > sixth term of an arithmetic progression is 23 and the sum of the first six terms is 78.Find<BR>\n" );
document.write( "(a)the common difference and the first term<BR>\n" );
document.write( "(b)the tenth term<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Since the sum of the six terms is 78 and the 6-th term is 23, the sum of the first 5 terms is 78-23 = 55.\r\n" );
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document.write( "In turn, it means that the 3-rd term, which is exactly in the middle of that five terms, is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2F5 ALIGN=MIDDLE  ALT=\"55%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 11.\r\n" );
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document.write( "Thus we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 11  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D ALIGN=MIDDLE  ALT=\"a%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 23.  The difference  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D ALIGN=MIDDLE  ALT=\"a%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > =   23-11 = 12 is exactly 3 times the common difference.\r\n" );
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document.write( "Hence, the common difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3 ALIGN=MIDDLE  ALT=\"12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Now you know ALL about this progression and can answer any question on your own.\r<BR>\n" );
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document.write( "On arithmetic progressions, see the introductory lessons \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( "in this site.\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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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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