document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983219>Question 983219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kindly solve and answer this one for me:\r<BR>\n" );
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document.write( "the sum of an infinite geometric series is 4 while the sum of all the terms is 192. What are the terms?\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604044 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52792)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let &nbsp;<B>a</B>&nbsp; be the first term of our geometric progression and &nbsp;<B>r</B>&nbsp; be its common ratio. \r<BR>\n" );
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document.write( "Then our first equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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" );
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document.write( "It is the formula for the sum of infinite geometric progression.\r<BR>\n" );
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document.write( "The sequence consisting of cubes of geometric progression is geometric progression itself, &nbsp;with the first term &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3 ALIGN=MIDDLE  ALT=\"a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp;  and the common ratio &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3 ALIGN=MIDDLE  ALT=\"r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;It is easy to check. \r<BR>\n" );
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document.write( "Therefore, &nbsp;the sum of such progression is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2F%281-r%5E3%29 ALIGN=MIDDLE  ALT=\"a%5E3%2F%281-r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It is our second equation.\r<BR>\n" );
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document.write( "Now, &nbsp;divide the second equation by the first one. &nbsp;You will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2F%281%2Br%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2%2F%281%2Br%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Thus you decreased the degree of the second equation from &nbsp;3&nbsp; to &nbsp;2.\r<BR>\n" );
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document.write( "Next, &nbsp;express the term &nbsp;<B>a</B>&nbsp; from the first equation as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%281-r%29 ALIGN=MIDDLE  ALT=\"4%2A%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and substitute it into the third equation. &nbsp;You will get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E2%2A%281-r%29%5E2%29%2F%281%2Br%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"%284%5E2%2A%281-r%29%5E2%29%2F%281%2Br%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-r%29%5E2 ALIGN=MIDDLE  ALT=\"%281-r%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%281%2Br%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"3%2A%281%2Br%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-2r+%2B+r%5E2 ALIGN=MIDDLE  ALT=\"1+-2r+%2B+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3r%5E2+%2B+3r+%2B3 ALIGN=MIDDLE  ALT=\"3r%5E2+%2B+3r+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It is a quadratic equation.\r<BR>\n" );
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document.write( "Would you solve it and complete the solution from this point?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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