document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162982>Question 1162982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What position (n) in the sequence is the following?<BR>\n" );
document.write( "tn = 680<BR>\n" );
document.write( "t1 = 104<BR>\n" );
document.write( "d = 16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786910 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=786910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "I will assume, based on the context and designations, &nbsp;that &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bk%5D ALIGN=MIDDLE  ALT=\"t%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;is an arithmetic progression.\r<BR>\n" );
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document.write( "Then the distance on the number line from the first to the last term is  &nbsp;680-104 = 576, &nbsp;and the number of intervals &nbsp;(gaps) &nbsp;between \r<BR>\n" );
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document.write( "the first and the last terms is  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576%2F16 ALIGN=MIDDLE  ALT=\"576%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 36.\r<BR>\n" );
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document.write( "Hence, the number &nbsp;680 &nbsp;is the &nbsp;37-th term of the sequence.\r<BR>\n" );
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document.write( "<U>ANSWER</U>.  &nbsp;&nbsp;n = 37.<BR>\n" );
document.write( "</pre>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "My lessons on arithmetic progressions in this site are\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/Chocolate-bars-and-arithmetic-progressions.lesson>Chocolate bars 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/Free-fall-and-arithmetic-progressions.lesson>Free fall 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/Uniformly-accelerated-motions-and-arithmetic-progressions.lesson>Uniformly accelerated motions 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/Increments-of-a-quadratic-function-form-an-arithmetic-progression.lesson>Increments of a quadratic function form an arithmetic progression</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( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Calculating-partial-sums-of-arithmetic-progressions.lesson>Calculating partial sums 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/Finding-number-of-terms-of-an-arithmeti--progression.lesson>Finding number of terms of an arithmetic progression</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/Advanced-problems-on-arithmetic-progressions.lesson>Advanced problems on 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/Interior-angles-of-a-polygon-and-Arithmetic-progression.lesson>Interior angles of a polygon and Arithmetic progression</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/Marh-Olimpiad-level-problem-on-arithmetic-progression.lesson>Math Olympiad level problem on arithmetic progression</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/Problems-on-arithmetic-progressions-solved-MENTALLY.lesson>Problems on arithmetic progressions solved MENTALLY</A> \r<BR>\n" );
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document.write( "The most relevant to your problem is the lesson marked (*) in the list.\r<BR>\n" );
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document.write( "Also, 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 <BR>\n" );
document.write( "<U>\"Arithmetic progressions\"</U>.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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