document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762771>Question 762771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all geometric sequences in which t3 + t4 = 36 and t5 + t6 = 144\r<BR>\n" );
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document.write( "I know one could be t1=3 t2=6 t3=12 t4=24 t5=48 t6=96\r<BR>\n" );
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document.write( "That would fit the question, but i'm assuming there's more than one geometric sequence that fits? There is two questions like this on my assignment. Don't know how to go about finding multiple sequences  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464363 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=464363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The way to solved it could be this one:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E2+%2B+Ar%5E3+=+36 ALIGN=MIDDLE  ALT=\"Ar%5E2+%2B+Ar%5E3+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E4+%2B+Ar%5E5+=+144 ALIGN=MIDDLE  ALT=\"Ar%5E4+%2B+Ar%5E5+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "These can be factored to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E2+%28r%2B1%29+=+36 ALIGN=MIDDLE  ALT=\"Ar%5E2+%28r%2B1%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E4+%28r%2B1%29+=144 ALIGN=MIDDLE  ALT=\"Ar%5E4+%28r%2B1%29+=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B1+=+36%2F%28Ar%5E2%29 ALIGN=MIDDLE  ALT=\"r%2B1+=+36%2F%28Ar%5E2%29\"   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%2B1+=+144%28Ar%5E4%29 ALIGN=MIDDLE  ALT=\"r%2B1+=+144%28Ar%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Setting these equal to each other and cross multiplying gives \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144Ar%5E2+=+36Ar%5E4 ALIGN=MIDDLE  ALT=\"144Ar%5E2+=+36Ar%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4Ar%5E2=Ar%5E4 ALIGN=MIDDLE  ALT=\"4Ar%5E2=Ar%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One solution is for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but that obviously won't work.<BR>\n" );
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document.write( "So, dividing through by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E2 ALIGN=MIDDLE  ALT=\"Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=r%5E2 ALIGN=MIDDLE  ALT=\"4=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Using these with the previous equations gives the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "and therefore the sequence.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A2%5E2+%2B+A%2A2%5E3+=+36 ALIGN=MIDDLE  ALT=\"A%2A2%5E2+%2B+A%2A2%5E3+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A+%2B+8A+=+36 ALIGN=MIDDLE  ALT=\"4A+%2B+8A+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12A+=+36 ALIGN=MIDDLE  ALT=\"12A+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+36%2F12 ALIGN=MIDDLE  ALT=\"A+=+36%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3 ALIGN=MIDDLE  ALT=\"A+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "same here\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A2%5E4+%2B+A%2A2%5E5+=+144 ALIGN=MIDDLE  ALT=\"A%2A2%5E4+%2B+A%2A2%5E5+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16A%2B32A=144 ALIGN=MIDDLE  ALT=\"16A%2B32A=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48A=144 ALIGN=MIDDLE  ALT=\"48A=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=144%2F48 ALIGN=MIDDLE  ALT=\"A=144%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3 ALIGN=MIDDLE  ALT=\"A=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "geometric sequences is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E0=t1=3%2A1=3+ ALIGN=MIDDLE  ALT=\"Ar%5E0=t1=3%2A1=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E1=t2=3%2A2=6+ ALIGN=MIDDLE  ALT=\"Ar%5E1=t2=3%2A2=6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E2=t3=+3%2A4=12 ALIGN=MIDDLE  ALT=\"Ar%5E2=t3=+3%2A4=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E3=t4=3%2A8=24 ALIGN=MIDDLE  ALT=\"Ar%5E3=t4=3%2A8=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E4=t5=3%2A16=48 ALIGN=MIDDLE  ALT=\"Ar%5E4=t5=3%2A16=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E5=t6=3%2A32=96 ALIGN=MIDDLE  ALT=\"Ar%5E5=t6=3%2A32=96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E6=t7=3%2A64=192 ALIGN=MIDDLE  ALT=\"Ar%5E6=t7=3%2A64=192\"   DISABLED_style= \"max-width:90%; height:auto;\" >...and so on\r<BR>\n" );
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document.write( "check if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t3+%2B+t4+=+36 ALIGN=MIDDLE  ALT=\"t3+%2B+t4+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t5+%2B+t6+=+144 ALIGN=MIDDLE  ALT=\"t5+%2B+t6+=+144\"   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=12+%2B+24+=+36 ALIGN=MIDDLE  ALT=\"12+%2B+24+=+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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48+%2B+96+=+144 ALIGN=MIDDLE  ALT=\"48+%2B+96+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144+=+144 ALIGN=MIDDLE  ALT=\"144+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );