document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598796>Question 598796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the geometric sequence find r and the 10th term.<BR>\n" );
document.write( "a) 4, 12, 36,108...<BR>\n" );
document.write( "b) 972, -324, 108, -36...\r<BR>\n" );
document.write( "\n" );
document.write( "Not really sure what to do here. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378708 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A geometric sequence is a sequence of numbers (called terms) where each number is the product of the one before times a fixed number, called the common ratio. So, with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=the nth term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=the term after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >=the common ratio<BR>\n" );
document.write( "we have the relations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2Ar ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D%2Fa%5Bn%5D=r ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D%2Fa%5Bn%5D=r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and if we call the first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "In 4, 12, 36,108... , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=4 ALIGN=MIDDLE  ALT=\"a%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=12%2F4=3 ALIGN=MIDDLE  ALT=\"r=12%2F4=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F12=3 ALIGN=MIDDLE  ALT=\"36%2F12=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F36=3 ALIGN=MIDDLE  ALT=\"108%2F36=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so applying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B10%5D=4%2A3%5E%2810-1%29=4%2A3%5E9=4%2A19683=78732 ALIGN=MIDDLE  ALT=\"a%5B10%5D=4%2A3%5E%2810-1%29=4%2A3%5E9=4%2A19683=78732\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "In 972, -324, 108, -36... , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=972 ALIGN=MIDDLE  ALT=\"a%5B1%5D=972\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=972%2F%28-324%29=-1%2F3 ALIGN=MIDDLE  ALT=\"r=972%2F%28-324%29=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so applying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B10%5D=972%2A%28-1%2F3%29%5E%2810-1%29=972%2A%28-1%2F3%29%5E9=-972%2A%281%2F3%5E9%29=-972%2F3%5E9=-4%2A3%5E5%2F3%5E9=-4%2F3%5E4=-4%2F81 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );