document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988607>Question 988607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fourth term of a geometric progression exceeds the third term by 54, and the sum of the second and third term is 36. Find the common ratio if it is positive </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609118 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=609118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the fourth term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D ALIGN=MIDDLE  ALT=\"a%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  exceeds the third term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54 ALIGN=MIDDLE  ALT=\"54\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D-a%5B3%5D+=54 ALIGN=MIDDLE  ALT=\"a%5B4%5D-a%5B3%5D+=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.1\r<BR>\n" );
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document.write( " if the sum of the second <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >and third term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D%2Ba%5B3%5D=36 ALIGN=MIDDLE  ALT=\"a%5B2%5D%2Ba%5B3%5D=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2\r<BR>\n" );
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document.write( "By using <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 have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ar%5E3-a%5B1%5D%2Ar%5E2=54 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ar%5E3-a%5B1%5D%2Ar%5E2=54\"   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%5B1%5D%2Ar%2Ba%5B1%5D%2Ar%5E2=36 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ar%2Ba%5B1%5D%2Ar%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2<BR>\n" );
document.write( "---------------------------------------------------add eq.2 and eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ar%5E3-a%5B1%5D%2Ar%5E2%2Ba%5B1%5D%2Ar%2Ba%5B1%5D%2Ar%5E2=54%2B36 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ar%5E3-a%5B1%5D%2Ar%5E2%2Ba%5B1%5D%2Ar%2Ba%5B1%5D%2Ar%5E2=54%2B36\"   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%2Ar%5E3%2Ba%5B1%5D%2Ar=90 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ar%5E3%2Ba%5B1%5D%2Ar=90\"   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%28r%5E3%2Br%29=90 ALIGN=MIDDLE  ALT=\"a%5B1%5D%28r%5E3%2Br%29=90\"   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=90%2F%28r%5E3%2Br%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D=90%2F%28r%5E3%2Br%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............substitute in eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2F%28r%5E3%2Br%29%2Ar%2B90%2F%28r%5E3%2Br%29%2Ar%5E2=36 ALIGN=MIDDLE  ALT=\"90%2F%28r%5E3%2Br%29%2Ar%2B90%2F%28r%5E3%2Br%29%2Ar%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90r%2F%28r%5E3%2Br%29%2B90r%5E2%2F%28r%5E3%2Br%29=36 ALIGN=MIDDLE  ALT=\"90r%2F%28r%5E3%2Br%29%2B90r%5E2%2F%28r%5E3%2Br%29=36\"   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=%2890r%2B190r%5E2%29=36%28r%5E3%2Br%29 ALIGN=MIDDLE  ALT=\"%2890r%2B190r%5E2%29=36%28r%5E3%2Br%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=90r%281%2Br%29=36r%28r%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"90r%281%2Br%29=36r%28r%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   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=5%281%2Br%29=2%28r%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"5%281%2Br%29=2%28r%5E2%2B1%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=5%2B5r=2r%5E2%2B2 ALIGN=MIDDLE  ALT=\"5%2B5r=2r%5E2%2B2\"   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=2r%5E2%2B2-5r-5=0 ALIGN=MIDDLE  ALT=\"2r%5E2%2B2-5r-5=0\"   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=2r%5E2-5r-3=0 ALIGN=MIDDLE  ALT=\"2r%5E2-5r-3=0\"   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=%28r-3%29+%282+r%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"%28r-3%29+%282+r%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> one solution will be: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28r-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=3%29 ALIGN=MIDDLE  ALT=\"highlight%28r=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> another solution will be: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%2B1=0 ALIGN=MIDDLE  ALT=\"2r%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r=-1 ALIGN=MIDDLE  ALT=\"2r=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=-1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28r=-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we can find first term:\r<BR>\n" );
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document.write( "if   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=3%29 ALIGN=MIDDLE  ALT=\"highlight%28r=3%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%5B1%5D%2A%283%29%2Ba%5B1%5D%2A%283%29%5E2=36 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2A%283%29%2Ba%5B1%5D%2A%283%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5B1%5D%2B9a%5B1%5D=36 ALIGN=MIDDLE  ALT=\"3a%5B1%5D%2B9a%5B1%5D=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%5B1%5D=36 ALIGN=MIDDLE  ALT=\"12a%5B1%5D=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=3%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=-1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28r=-1%2F2%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%5B1%5D%2A%28-1%2F2%29%2Ba%5B1%5D%2A%28-1%2F2%29%5E2=36 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2A%28-1%2F2%29%2Ba%5B1%5D%2A%28-1%2F2%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2A%28-1%2F2%29%2Ba%5B1%5D%2A%281%2F4%29=36 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2A%28-1%2F2%29%2Ba%5B1%5D%2A%281%2F4%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >......multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=-2a%5B1%5D%2Ba%5B1%5D=144 ALIGN=MIDDLE  ALT=\"-2a%5B1%5D%2Ba%5B1%5D=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%5B1%5D=144 ALIGN=MIDDLE  ALT=\"-a%5B1%5D=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=+-144%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=+-144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, there are two solutions:<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=3%29 ALIGN=MIDDLE  ALT=\"highlight%28r=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=+-144%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=+-144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=-1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28r=-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then the second term is:\r<BR>\n" );
document.write( "\n" );
document.write( "if <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;\" > and <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( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=3%2A3 ALIGN=MIDDLE  ALT=\"a%5B2%5D=3%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=9 ALIGN=MIDDLE  ALT=\"a%5B2%5D=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "third term is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=3%2A3%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D=3%2A3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=27 ALIGN=MIDDLE  ALT=\"a%5B3%5D=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "fourth term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=3%2A3%5E3 ALIGN=MIDDLE  ALT=\"a%5B4%5D=3%2A3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=3%2A27 ALIGN=MIDDLE  ALT=\"a%5B4%5D=3%2A27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=81 ALIGN=MIDDLE  ALT=\"a%5B4%5D=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the terms of sequence are:=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2C9%2C27%2C81 ALIGN=MIDDLE  ALT=\"3%2C9%2C27%2C81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-144 ALIGN=MIDDLE  ALT=\"a=-144\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-1%2F2 ALIGN=MIDDLE  ALT=\"r=-1%2F2\"   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%5B2%5D=+-144%2A%28-1%2F2%29%5E1 ALIGN=MIDDLE  ALT=\"a%5B2%5D=+-144%2A%28-1%2F2%29%5E1\"   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%5B2%5D=-144%2F-2 ALIGN=MIDDLE  ALT=\"a%5B2%5D=-144%2F-2\"   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%5B2%5D=72 ALIGN=MIDDLE  ALT=\"a%5B2%5D=72\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "third term is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=-144%2A%28-1%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D=-144%2A%28-1%2F2%29%5E2\"   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%5B3%5D=+-144%281%2F4%29 ALIGN=MIDDLE  ALT=\"a%5B3%5D=+-144%281%2F4%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%5B3%5D=+-36 ALIGN=MIDDLE  ALT=\"a%5B3%5D=+-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and fourth term is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=+-144%2A%28-1%2F2%29%5E3 ALIGN=MIDDLE  ALT=\"a%5B4%5D=+-144%2A%28-1%2F2%29%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%5B4%5D=+-144%28-1%2F8%29 ALIGN=MIDDLE  ALT=\"a%5B4%5D=+-144%28-1%2F8%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%5B4%5D=18 ALIGN=MIDDLE  ALT=\"a%5B4%5D=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the terms of sequence are:=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-144%2C72%2C-36%2C18 ALIGN=MIDDLE  ALT=\"-144%2C72%2C-36%2C18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now, check given data:\r<BR>\n" );
document.write( "\n" );
document.write( "for =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2C9%2C27%2C81 ALIGN=MIDDLE  ALT=\"3%2C9%2C27%2C81\"   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%5B4%5D=a%5B3%5D+%2B54 ALIGN=MIDDLE  ALT=\"a%5B4%5D=a%5B3%5D+%2B54\"   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=81=27+%2B54 ALIGN=MIDDLE  ALT=\"81=27+%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=81 ALIGN=MIDDLE  ALT=\"81=81\"   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%5B2%5D%2Ba%5B3%5D=36 ALIGN=MIDDLE  ALT=\"a%5B2%5D%2Ba%5B3%5D=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B27=36 ALIGN=MIDDLE  ALT=\"9%2B27=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=36 ALIGN=MIDDLE  ALT=\"36=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-144%2C72%2C-36%2C18 ALIGN=MIDDLE  ALT=\"-144%2C72%2C-36%2C18\"   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%5B4%5D=a%5B3%5D+%2B54 ALIGN=MIDDLE  ALT=\"a%5B4%5D=a%5B3%5D+%2B54\"   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=18=-36+%2B54 ALIGN=MIDDLE  ALT=\"18=-36+%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=18 ALIGN=MIDDLE  ALT=\"18=18\"   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%5B2%5D%2Ba%5B3%5D=36 ALIGN=MIDDLE  ALT=\"a%5B2%5D%2Ba%5B3%5D=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2B%28-36%29=36 ALIGN=MIDDLE  ALT=\"72%2B%28-36%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=36 ALIGN=MIDDLE  ALT=\"36=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );