document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121106>Question 121106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What function represents the geometric sequence ( 3,15,75,375,...)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88840 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=88840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Notice that each term is increasing exponentially. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.\r<BR>\n" );
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document.write( "First divide the 2nd term 15 by the 1st term 3 to get  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F3=5 ALIGN=MIDDLE  ALT=\"15%2F3=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now divide the 3rd term 75 by the 2nd term 15 to get  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F15=5 ALIGN=MIDDLE  ALT=\"75%2F15=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now divide the 4th term 375 by the 3rd term 75 to get  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=375%2F75=5 ALIGN=MIDDLE  ALT=\"375%2F75=5\"   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 if we pick any term and divide it by the previous term, we'll always get 5. This is the common ratio between the terms. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now since we've started at 3, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the general geometric sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=ar%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=ar%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means the sequence is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%2A5%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A5%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Notice when n=0, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D=3%2A5%5E0=3%2A1=3 ALIGN=MIDDLE  ALT=\"a%5B0%5D=3%2A5%5E0=3%2A1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and when n=1, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=3%2A5%5E1=3%2A5=15 ALIGN=MIDDLE  ALT=\"a%5B1%5D=3%2A5%5E1=3%2A5=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and when n=2, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=3%2A5%5E2=3%2A25=75 ALIGN=MIDDLE  ALT=\"a%5B2%5D=3%2A5%5E2=3%2A25=75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and when n=3, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=3%2A5%5E3=3%2A125=375 ALIGN=MIDDLE  ALT=\"a%5B3%5D=3%2A5%5E3=3%2A125=375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and so on.... </SPAN>\n" );
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