document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3840>Question 3840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the numbers a, b, c are the terms of a geometric sequence so that <BR>\n" );
document.write( "a+b+c=35 and abc=1000\r<BR>\n" );
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document.write( "find a, b and c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1679 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a nice little question :-)\r<BR>\n" );
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document.write( "Let first term = a<BR>\n" );
document.write( "then second term = ar<BR>\n" );
document.write( "and third term = <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;\" >\r<BR>\n" );
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document.write( "where r is the common ratio.\r<BR>\n" );
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document.write( "And we know that all 3 terms multiplied together = 1000. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28ar%29%28ar%5E2%29+=+1000 ALIGN=MIDDLE  ALT=\"a%28ar%29%28ar%5E2%29+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3r%5E3+=+1000 ALIGN=MIDDLE  ALT=\"a%5E3r%5E3+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ar%29%5E3+1000 ALIGN=MIDDLE  ALT=\"%28ar%29%5E3+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--> ar = cube root of 1000<BR>\n" );
document.write( "ie ar = 10.\r<BR>\n" );
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document.write( "And ar, by definition is the number b. So we have one found.\r<BR>\n" );
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document.write( "Since abc = 1000 and b=10, then ac=100. We shall use this in a moment.\r<BR>\n" );
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document.write( "Also, a+b+c=35. So now this becomes a+c=25 or a=25-c. Now sub this into the ac=100, to give (25-c)c=100.\r<BR>\n" );
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document.write( "Multiplying this out, we get a quadratic, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-25c%2B100=0 ALIGN=MIDDLE  ALT=\"c%5E2-25c%2B100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which factorises to (c-5)(c-20)=0, so c=5 or c=20. This means that a=20 or a=5...ie the reverse solution. So,\r<BR>\n" );
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document.write( "a=5<BR>\n" );
document.write( "b=10<BR>\n" );
document.write( "c=20\r<BR>\n" );
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document.write( "Common ratio is 2.<BR>\n" );
document.write( "and Adding them --> 35<BR>\n" );
document.write( "multiplying them --> 1000.\r<BR>\n" );
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document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
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