document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190609>Question 190609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> # 1. Use inductive reasoning to determine the next three numbers in the pattern: 1,  1/3,  1/9,  1/27, ...  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143068 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1 \r<BR>\n" );
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document.write( "Q: <font color=red> Use inductive reasoning to determine the next three numbers in the pattern: 1,  1/3,  1/9,  1/27, ... </font>\r<BR>\n" );
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document.write( "A:\r<BR>\n" );
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document.write( "From the first term 1 to the second term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, notice how the second term is just the first term divided by 3. So let's see if this holds from the second term to the third term.\r<BR>\n" );
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document.write( "If we divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2F3=%281%2F3%29%281%2F3%29=1%2F%283%2A3%29=1%2F9 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2F3=%281%2F3%29%281%2F3%29=1%2F%283%2A3%29=1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this shows that if we divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F9%29%2F3=%281%2F9%29%281%2F3%29=1%2F%289%2A3%29=1%2F27 ALIGN=MIDDLE  ALT=\"%281%2F9%29%2F3=%281%2F9%29%281%2F3%29=1%2F%289%2A3%29=1%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F27 ALIGN=MIDDLE  ALT=\"1%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So using inductive reasoning, we would conjecture that this pattern continues indefinitely. \r<BR>\n" );
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document.write( "So this means that we can find the next three terms by dividing each previous term by 3.\r<BR>\n" );
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document.write( "So divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F27 ALIGN=MIDDLE  ALT=\"1%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 3 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F27%29%2F3=%281%2F27%29%281%2F3%29=1%2F%2827%2A3%29=1%2F81 ALIGN=MIDDLE  ALT=\"%281%2F27%29%2F3=%281%2F27%29%281%2F3%29=1%2F%2827%2A3%29=1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the next term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F81 ALIGN=MIDDLE  ALT=\"1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F81 ALIGN=MIDDLE  ALT=\"1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 3 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F81%29%2F3=%281%2F81%29%281%2F3%29=1%2F%2881%2A3%29=1%2F243 ALIGN=MIDDLE  ALT=\"%281%2F81%29%2F3=%281%2F81%29%281%2F3%29=1%2F%2881%2A3%29=1%2F243\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the next term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F243 ALIGN=MIDDLE  ALT=\"1%2F243\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------\r<BR>\n" );
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document.write( "So divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F243 ALIGN=MIDDLE  ALT=\"1%2F243\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 3 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F243%29%2F3=%281%2F243%29%281%2F3%29=1%2F%28243%2A3%29=1%2F729 ALIGN=MIDDLE  ALT=\"%281%2F243%29%2F3=%281%2F243%29%281%2F3%29=1%2F%28243%2A3%29=1%2F729\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the next term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F729 ALIGN=MIDDLE  ALT=\"1%2F729\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "======================\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the next three terms of the sequence are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F81 ALIGN=MIDDLE  ALT=\"1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F243 ALIGN=MIDDLE  ALT=\"1%2F243\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F729 ALIGN=MIDDLE  ALT=\"1%2F729\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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