document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085662>Question 1085662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the 3rd term of a linear sequence is twice the 1st term and the 8th term of the sequence is four more than the 6th term. find the first term of the arithmetic progression.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699732 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52800)</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=699732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Since \"the 8th term of the sequence is four more than the 6th term\", it implies that the common difference is half of 4, i.e. d = 2.\r\n" );
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document.write( "Since \"the 3rd term of a linear sequence is twice the 1st term\", it means that\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B2%2A2 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa%5B1%5D ALIGN=MIDDLE  ALT=\"2%2Aa%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,   or\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B4 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5B1%5D ALIGN=MIDDLE  ALT=\"2a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "Hence, <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;\" > = 4.\r\n" );
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document.write( "Thus the first term of the AP is 4 and the common difference is 2.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Notice that the term \"linear sequence\" is out of use. The canonical term is Arithmetic progression on Arithmetic sequence.\r<BR>\n" );
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document.write( "On arithmetic progressions, see the lessons 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( " </SPAN>\n" );
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