document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=659640>Question 659640</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the nth term of the geometric sequence<BR>\n" );
document.write( "125,25,5,1...\r<BR>\n" );
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document.write( "Find the nth term of the geometric sequence<BR>\n" );
document.write( "7,49,343,2401,... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410855 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=410855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the nth term of the geometric sequence<BR>\n" );
document.write( "125,25,5,1...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >...every next one is divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "nth of General Term of a Geometric Sequence: <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" );
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document.write( "where <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;\" > is the first term of the sequence and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common ratio.\r<BR>\n" );
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document.write( "We have the common ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F5 ALIGN=MIDDLE  ALT=\"r=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=125 ALIGN=MIDDLE  ALT=\"a%5B1%5D=125\"   DISABLED_style= \"max-width:90%; height:auto;\" >,then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%5D=125%2A%281%2F5%29%5E%28n-1%29%29+ ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%5D=125%2A%281%2F5%29%5E%28n-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, check sixth term above using this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=125%2A%281%2F5%29%5E%286-1%29+ ALIGN=MIDDLE  ALT=\"a%5B6%5D=125%2A%281%2F5%29%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=a%5B6%5D=125%2A%281%2F5%29%5E5+ ALIGN=MIDDLE  ALT=\"a%5B6%5D=125%2A%281%2F5%29%5E5+\"   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=125%2A%281%2F25%29=0.04+ ALIGN=MIDDLE  ALT=\"a%5B6%5D=125%2A%281%2F25%29=0.04+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the nth term of the geometric sequence<BR>\n" );
document.write( "7,49,343,2401,...<BR>\n" );
document.write( "it is a \"geometric sequence\" which that means that each successive term is multiplied by the same factor, and in this sequence the common factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=7 ALIGN=MIDDLE  ALT=\"f=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Geometric sequences have an nth term of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=+a%5B1%5Df%5E%28n-1%29+ ALIGN=MIDDLE  ALT=\"a%5Bn%5D=+a%5B1%5Df%5E%28n-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <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;\" > is the first term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common factor and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of the term (nth term).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%5D=+a%5B1%5D7%5E%28n-1%29%29+ ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%5D=+a%5B1%5D7%5E%28n-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=7 ALIGN=MIDDLE  ALT=\"a%5B1%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=7 ALIGN=MIDDLE  ALT=\"f=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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