document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807576>Question 807576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 respectively. Find the difference between the largest and smallest terms of the three numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486389 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=486389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 respectively. Find the difference between the largest and smallest terms of the three numbers<BR>\n" );
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document.write( "Product: (a*ar*ar^2) = 3375<BR>\n" );
document.write( "(ar)^3 = 3375<BR>\n" );
document.write( "ar = 15<BR>\n" );
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document.write( "Sum::::: (a + ar + ar^2) = 65<BR>\n" );
document.write( "(a + ar + ar*r) = 65<BR>\n" );
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document.write( "Substitute for ar in the sum to get<BR>\n" );
document.write( "(a + 15 + 15r) = 65<BR>\n" );
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document.write( "Two Equations::<BR>\n" );
document.write( "ar = 15<BR>\n" );
document.write( "a + 15r = 50<BR>\n" );
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document.write( "Substitute for \"a\" and solve for \"r\":<BR>\n" );
document.write( "(50-15r)r = 15<BR>\n" );
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document.write( "15r^2 - 50r + 15 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "3r^2 - 10r + 3 = 0<BR>\n" );
document.write( "Factor: <BR>\n" );
document.write( "3r^2-9r-r+3 = 0<BR>\n" );
document.write( "3r(r-3)-(r-3) = 0<BR>\n" );
document.write( "(r-3)(3x-1) = 0<BR>\n" );
document.write( "===<BR>\n" );
document.write( "r = 3 or r = 1/3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "If r = 3, a = 5 : Then ar^2 = 45:: Then difference = 45-5 = 40<BR>\n" );
document.write( "If r = 1/3, a = 45: Then ar^2 = 5:: Then diffeerence = 5-45 = -40<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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