document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157839>Question 1157839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given two terms in a geometric sequence find the term named in the problem and the explicit formula\r<BR>\n" );
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document.write( "http://prntscr.com/s9icre </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780799 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "23.\r<BR>\n" );
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document.write( "a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can also calculate any term using the Rule:\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=-128 ALIGN=MIDDLE  ALT=\"a%5B6%5D=-128\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=a%5B1%5D%2Ar%5E%286-1%29 ALIGN=MIDDLE  ALT=\"a%5B6%5D=a%5B1%5D%2Ar%5E%286-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128=a%5B1%5D%2Ar%5E5 ALIGN=MIDDLE  ALT=\"-128=a%5B1%5D%2Ar%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >........solve for <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-128%2Fr%5E5 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-128%2Fr%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=-16 ALIGN=MIDDLE  ALT=\"a%5B3%5D=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=3 ALIGN=MIDDLE  ALT=\"n=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=a%5B1%5D%2Ar%5E%283-1%29 ALIGN=MIDDLE  ALT=\"a%5B3%5D=a%5B1%5D%2Ar%5E%283-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16=a%5B1%5D%2Ar%5E2 ALIGN=MIDDLE  ALT=\"-16=a%5B1%5D%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........solve for <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-16%2Fr%5E2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-16%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.2\r<BR>\n" );
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document.write( "from eq.1 and eq.2 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128%2Fr%5E5=-16%2Fr%5E2 ALIGN=MIDDLE  ALT=\"-128%2Fr%5E5=-16%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128r%5E2=-16r%5E5 ALIGN=MIDDLE  ALT=\"-128r%5E2=-16r%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128=-16r%5E3 ALIGN=MIDDLE  ALT=\"-128=-16r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=-128%2F-16 ALIGN=MIDDLE  ALT=\"r%5E3=-128%2F-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=8 ALIGN=MIDDLE  ALT=\"r%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=2%5E3 ALIGN=MIDDLE  ALT=\"r%5E3=2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-16%2Fr%5E2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-16%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.2, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-16%2F2%5E2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-16%2F2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-16%2F4 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-16%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "nth term formula 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=%28-4%29%2A2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%28-4%29%2A2%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D ALIGN=MIDDLE  ALT=\"a%5B12%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D=%28-4%29%2A2%5E%2812-1%29 ALIGN=MIDDLE  ALT=\"a%5B12%5D=%28-4%29%2A2%5E%2812-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D=%28-4%29%2A2%5E11 ALIGN=MIDDLE  ALT=\"a%5B12%5D=%28-4%29%2A2%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D=%28-4%29%2A2048 ALIGN=MIDDLE  ALT=\"a%5B12%5D=%28-4%29%2A2048\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B12%5D=-8192 ALIGN=MIDDLE  ALT=\"a%5B12%5D=-8192\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "24.\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=48 ALIGN=MIDDLE  ALT=\"a%5B5%5D=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48=a%5B1%5D%2Ar%5E%285-1%29 ALIGN=MIDDLE  ALT=\"48=a%5B1%5D%2Ar%5E%285-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48=a%5B1%5D%2Ar%5E4 ALIGN=MIDDLE  ALT=\"48=a%5B1%5D%2Ar%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=48%2Fr%5E4 ALIGN=MIDDLE  ALT=\"a%5B1%5D=48%2Fr%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=24 ALIGN=MIDDLE  ALT=\"a%5B4%5D=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=a%5B1%5D%2Ar%5E%284-1%29 ALIGN=MIDDLE  ALT=\"24=a%5B1%5D%2Ar%5E%284-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=a%5B1%5D%2Ar%5E3 ALIGN=MIDDLE  ALT=\"24=a%5B1%5D%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=24%2Fr%5E3 ALIGN=MIDDLE  ALT=\"a%5B1%5D=24%2Fr%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2\r<BR>\n" );
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document.write( "from eq.1 and eq.2 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fr%5E4=24%2Fr%5E3 ALIGN=MIDDLE  ALT=\"48%2Fr%5E4=24%2Fr%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48r%5E3=24r%5E4 ALIGN=MIDDLE  ALT=\"48r%5E3=24r%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48=24r ALIGN=MIDDLE  ALT=\"48=24r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=48%2F24 ALIGN=MIDDLE  ALT=\"r=48%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=24%2Fr%5E3 ALIGN=MIDDLE  ALT=\"a%5B1%5D=24%2Fr%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=24%2F2%5E3 ALIGN=MIDDLE  ALT=\"a%5B1%5D=24%2F2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=24%2F8 ALIGN=MIDDLE  ALT=\"a%5B1%5D=24%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \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 ALIGN=MIDDLE  ALT=\"a%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "then,\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%2A2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A2%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B9%5D ALIGN=MIDDLE  ALT=\"a%5B9%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=9 ALIGN=MIDDLE  ALT=\"n=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B9%5D=3%2A2%5E%289-1%29 ALIGN=MIDDLE  ALT=\"a%5B9%5D=3%2A2%5E%289-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B9%5D=3%2A2%5E8 ALIGN=MIDDLE  ALT=\"a%5B9%5D=3%2A2%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B9%5D=3%2A256 ALIGN=MIDDLE  ALT=\"a%5B9%5D=3%2A256\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B9%5D=768 ALIGN=MIDDLE  ALT=\"a%5B9%5D=768\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );