document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209818>Question 1209818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850681 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The AI solution from the other \"tutor\" has the right final answer, but the AI presentation is hard to follow.  Here is a solution in English....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%29=1 ALIGN=MIDDLE  ALT=\"a%280%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282%29=2 ALIGN=MIDDLE  ALT=\"a%282%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28n%2B2%29=a%28n%2B1%29%2Fa%28n%29 ALIGN=MIDDLE  ALT=\"a%28n%2B2%29=a%28n%2B1%29%2Fa%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Although the given starting information is not standard, we can use the recursive definition with the given values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%29 ALIGN=MIDDLE  ALT=\"a%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282%29 ALIGN=MIDDLE  ALT=\"a%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29 ALIGN=MIDDLE  ALT=\"a%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then use the recursive definition to find all subsequent terms.<br><BR>\n" );
document.write( "For n=0....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282%29=a%281%29%2Fa%280%29 ALIGN=MIDDLE  ALT=\"a%282%29=a%281%29%2Fa%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=a%281%29%2F1 ALIGN=MIDDLE  ALT=\"2=a%281%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29=2 ALIGN=MIDDLE  ALT=\"a%281%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the first three terms are 1, 2, and 2.<br><BR>\n" );
document.write( "Note that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%280%29 ALIGN=MIDDLE  ALT=\"a%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem asks for the sum of the terms through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28100%29 ALIGN=MIDDLE  ALT=\"a%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we are looking for the sum of the first 101 terms.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%283%29=a%282%29%2Fa%281%29=2%2F2=1 ALIGN=MIDDLE  ALT=\"a%283%29=a%282%29%2Fa%281%29=2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284%29=a%283%29%2Fa%282%29=1%2F2=1%2F2 ALIGN=MIDDLE  ALT=\"a%284%29=a%283%29%2Fa%282%29=1%2F2=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%285%29=a%284%29%2Fa%283%29=%281%2F2%29%2F1=1%2F2 ALIGN=MIDDLE  ALT=\"a%285%29=a%284%29%2Fa%283%29=%281%2F2%29%2F1=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%286%29=a%285%29%2Fa%284%29=%281%2F2%29%2F%281%2F2%29=1 ALIGN=MIDDLE  ALT=\"a%286%29=a%285%29%2Fa%284%29=%281%2F2%29%2F%281%2F2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%287%29=a%286%29%2Fa%285%29=1%2F%281%2F2%29=2 ALIGN=MIDDLE  ALT=\"a%287%29=a%286%29%2Fa%285%29=1%2F%281%2F2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%288%29=a%287%29%2Fa%286%29=2%2F1=1 ALIGN=MIDDLE  ALT=\"a%288%29=a%287%29%2Fa%286%29=2%2F1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We now see that the terms of the sequence follow a cyclic pattern of length 6:<br><BR>\n" );
document.write( "1, 2, 2, 1, 1/2, 1/2<br><BR>\n" );
document.write( "With a cycle of length 6, 101 terms will mean 16 times through the cycle plus 5 more terms.<br><BR>\n" );
document.write( "The sum of the numbers in each cycle is 7; the sum of the numbers in 16 cycles is 16*7 = 112.<BR>\n" );
document.write( "The sum of the first 5 numbers in each cycle is 6.5.<BR>\n" );
document.write( "The sum of the first 101 terms is 112+6.5 = 118.5<br><BR>\n" );
document.write( "ANSWER: 118.5<br><BR>\n" );
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