document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117751>Question 117751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2, 6 , 18 , 54 , ....<BR>\n" );
document.write( " In the sequence above what would be the 8th term? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85721 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=85721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice that each term is increasing quickly. 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( "\n" );
document.write( "First divide the 2nd term 6 by the 1st term 2 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2=3 ALIGN=MIDDLE  ALT=\"6%2F2=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 18 by the 2nd term 6 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F6=3 ALIGN=MIDDLE  ALT=\"18%2F6=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 54 by the 3rd term 18 to get  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2F18=3 ALIGN=MIDDLE  ALT=\"54%2F18=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. 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( "\n" );
document.write( "Now since we've started at 2, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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=2%2A3%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=2%2A3%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice if we let n=0, we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D=2%2A3%5E0=2%2A1=2 ALIGN=MIDDLE  ALT=\"a%5B0%5D=2%2A3%5E0=2%2A1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice this is the first term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and if we let n=1, we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=2%2A3%5E1=2%2A3=6 ALIGN=MIDDLE  ALT=\"a%5B1%5D=2%2A3%5E1=2%2A3=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice this is the second term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and this generates the sequence 2, 6 , 18 , 54 , ....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So to find the 8th term, let n=7 (remember, we started at n=0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B7%5D=2%2A3%5E7=2%2A2187=4374 ALIGN=MIDDLE  ALT=\"a%5B7%5D=2%2A3%5E7=2%2A2187=4374\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in n=7 and simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the eighth term is 4,374<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );