document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286343>Question 286343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three numbers in geometric progression whose sum is 21 and sum of their squares is 189? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207661 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Geometric Progression means that the numbers are multiples. For example:\r<BR>\n" );
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document.write( "2,4,8 is a geometric progression, because 2x2=4, and then 2x4=8. The next number in the progression would be 8x2=16. The number that you multiply by is called the common ratio. In this case, the common ratio is 2.\r<BR>\n" );
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document.write( "For your question, you need to find x, the first number, and r, the common ratio. Let's set up the equations:\r<BR>\n" );
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document.write( "Eqn.1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+rx+%2B+r%5E2x+=+21 ALIGN=MIDDLE  ALT=\"x+%2B+rx+%2B+r%5E2x+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that the r^2 term comes from multiplying by the common ratio a 2nd time to get the 3rd number.\r<BR>\n" );
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document.write( "Eqn. 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28rx%29%5E2+%2B+%28%28r%5E2%29x%29+=+189 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28rx%29%5E2+%2B+%28%28r%5E2%29x%29+=+189\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm not sure what level of math this is. Do you know how to solve equations like this? \r<BR>\n" );
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document.write( "I will give you the answer, and hopefully you can work it out. Let me know if you'd like some extra help. \r<BR>\n" );
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document.write( "The common ratio, r=2, and the first number x=3.\r<BR>\n" );
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document.write( "The three numbers are 3, 6 and 12.\r<BR>\n" );
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document.write( "3+6+12=21\r<BR>\n" );
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document.write( "3^2+6^2+12^2=9+36+144=189 </SPAN>\n" );
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