document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202544>Question 202544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can ANYONE help me with these two problems? Please!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Type the general term for the following sequences:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#1) 3, 9, 27, 81, 243, . . .<BR>\n" );
document.write( "__________\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#2) 3/4, 6/5, 9/6, 12/7, 15/8...<BR>\n" );
document.write( "__________\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thanks,<BR>\n" );
document.write( "Sarah </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152745 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=152745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you going\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "# 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First divide the 2nd term 9 by the 1st term 3 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F3=3 ALIGN=MIDDLE  ALT=\"9%2F3=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "Now divide the 3rd term 27 by the 2nd term 9 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2F9=3 ALIGN=MIDDLE  ALT=\"27%2F9=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "Now divide the 4th term 81 by the 3rd term 27 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F27=3 ALIGN=MIDDLE  ALT=\"81%2F27=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "Now divide the 5th term 243 by the 4th term 81 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=243%2F81=3 ALIGN=MIDDLE  ALT=\"243%2F81=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "So if we pick ANY term and divide it by the previous term, we'll always get 3. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "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=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%2A3%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A3%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > starts at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "===============================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%2A3%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A3%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > starts at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: if you want to start at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you need to replace \"n\" with \"n-1\" to get the new sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%2A3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );