document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957592>Question 957592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the first 3 items of a geometric progression are a &#8722; 1, a +3, and 3 a +1 for some positive<BR>\n" );
document.write( "number a, what is the numerical value of the fourth term? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585177 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=585177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
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document.write( "the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms of a geometric progression are <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-1 ALIGN=MIDDLE  ALT=\"a-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B3 ALIGN=MIDDLE  ALT=\"a+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B1 ALIGN=MIDDLE  ALT=\"3a+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "for some positive number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In a Geometric Sequence each term is found by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=multiplying ALIGN=MIDDLE  ALT=\"multiplying\"   DISABLED_style= \"max-width:90%; height:auto;\" > the previous term by a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=constant ALIGN=MIDDLE  ALT=\"constant\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Let a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=constant ALIGN=MIDDLE  ALT=\"constant\"   DISABLED_style= \"max-width:90%; height:auto;\" > be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=%28a+-1%29k=+a+%2B3 ALIGN=MIDDLE  ALT=\"%28a+-1%29k=+a+%2B3\"   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=k=+%28a+%2B3%29%2F%28a+-1%29 ALIGN=MIDDLE  ALT=\"k=+%28a+%2B3%29%2F%28a+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........(1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B3%29k=+3a+%2B1 ALIGN=MIDDLE  ALT=\"%28a+%2B3%29k=+3a+%2B1\"   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=k=+%283a+%2B1%29%2F%28a+%2B3%29 ALIGN=MIDDLE  ALT=\"k=+%283a+%2B1%29%2F%28a+%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........(2)\r<BR>\n" );
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document.write( "make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29=%282%29 ALIGN=MIDDLE  ALT=\"%281%29=%282%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=%28a+%2B3%29%2F%28a+-1%29=%283a+%2B1%29%2F%28a+%2B3%29 ALIGN=MIDDLE  ALT=\"%28a+%2B3%29%2F%28a+-1%29=%283a+%2B1%29%2F%28a+%2B3%29\"   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=%28a+%2B3%29%28a+%2B3%29=%283a+%2B1%29%28a+-1%29 ALIGN=MIDDLE  ALT=\"%28a+%2B3%29%28a+%2B3%29=%283a+%2B1%29%28a+-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%5E2+%2B3a+%2B3a%2B9=3a%5E2-3a+%2Ba+-1 ALIGN=MIDDLE  ALT=\"a%5E2+%2B3a+%2B3a%2B9=3a%5E2-3a+%2Ba+-1\"   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%5E2+%2B6a%2B9=3a%5E2-2a+-1 ALIGN=MIDDLE  ALT=\"a%5E2+%2B6a%2B9=3a%5E2-2a+-1\"   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=0=3a%5E2-2a+-1-a%5E2+-6a-9 ALIGN=MIDDLE  ALT=\"0=3a%5E2-2a+-1-a%5E2+-6a-9\"   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=2a%5E2-8a+-10+=0 ALIGN=MIDDLE  ALT=\"2a%5E2-8a+-10+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-4a+-5=0 ALIGN=MIDDLE  ALT=\"a%5E2-4a+-5=0\"   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%5E2%2Ba-5a+-5=0 ALIGN=MIDDLE  ALT=\"a%5E2%2Ba-5a+-5=0\"   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=%28a%5E2%2Ba%29-%285a+%2B5%29=0 ALIGN=MIDDLE  ALT=\"%28a%5E2%2Ba%29-%285a+%2B5%29=0\"   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%28a%2B1%29-5%28a+%2B1%29=0 ALIGN=MIDDLE  ALT=\"a%28a%2B1%29-5%28a+%2B1%29=0\"   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=%28a-5%29%28a+%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28a-5%29%28a+%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since given that first 3 terms are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-1 ALIGN=MIDDLE  ALT=\"a+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B3 ALIGN=MIDDLE  ALT=\"a+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B1 ALIGN=MIDDLE  ALT=\"3a+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, our solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your terms are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-1=5-1=4 ALIGN=MIDDLE  ALT=\"a+-1=5-1=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B3=5%2B8=8 ALIGN=MIDDLE  ALT=\"a+%2B3=5%2B8=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B1=3%2A5%2B1=16 ALIGN=MIDDLE  ALT=\"3a+%2B1=3%2A5%2B1=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=k=+%28a+%2B3%29%2F%28a+-1%29 ALIGN=MIDDLE  ALT=\"k=+%28a+%2B3%29%2F%28a+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=+8%2F4 ALIGN=MIDDLE  ALT=\"k=+8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=+2 ALIGN=MIDDLE  ALT=\"k=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the fourth term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A16=32 ALIGN=MIDDLE  ALT=\"2%2A16=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );