document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098950>Question 1098950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.The 4th and 6th term of an A.P is 6 and 24 respectively. Find (1) the sum of the first seven term (ii) the eight term<BR>\n" );
document.write( "2.solve the following quadratically (1)x square-5x-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713360 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52847)</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=713360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Between the 6th and 4th terms of an AP there is the room for two common differencies;\r\n" );
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document.write( "therefore, the common difference d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%28a%5B6%5D-a%5B4%5D%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%28a%5B6%5D-a%5B4%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%2824-6%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%2824-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9.\r\n" );
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document.write( "In more formal way,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D-a%5B4%5D ALIGN=MIDDLE  ALT=\"a%5B6%5D-a%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2B5d%29 ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2B5d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2B3d%29 ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2B3d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2d = 24 - 6 = 18,  hence,  d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F2 ALIGN=MIDDLE  ALT=\"18%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9.\r\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D-3d ALIGN=MIDDLE  ALT=\"a%5B4%5D-3d\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6 - 3*9 = -21.\r\n" );
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document.write( "As you know now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and d, you actually know EVERYTHING about the given AP.\r\n" );
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document.write( "For example,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B7%5D ALIGN=MIDDLE  ALT=\"a%5B7%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B6%2Ad ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B6%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -21 + 6*9 = 33.\r\n" );
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document.write( "Now, the sum of the first 7 terms is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B7%5D ALIGN=MIDDLE  ALT=\"S%5B7%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%5B1%5D%2Ba%5B7%5D%29%2F2%29%2A7 ALIGN=MIDDLE  ALT=\"%28%28a%5B1%5D%2Ba%5B7%5D%29%2F2%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-21%2B33%29%2F2%29%2A7 ALIGN=MIDDLE  ALT=\"%28%28-21%2B33%29%2F2%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 42.\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%2A9 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B7%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -21+ 7*9 = 42.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "-------------------<BR>\n" );
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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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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document.write( " </SPAN>\n" );
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