document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408537>Question 408537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the first two terms of a seven-term GP (geometric progression) is 20 and the sum of the last two terms is -5/8.  Find the sum of all seven terms.\r<BR>\n" );
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document.write( "I know that a GP is one in which the ratio obtained by dividing any term by the preceding term is always the same.  I also know the formula for finding the nth term in a geometric sequence.  The first thing I tried was to let x = the first term.  Then (20 - x) = the second term.  Additionally, I let y = the next to the last term and (-5/8 - y) = the last term.  Since the ratio by dividing any term by the preceding term is always the same, I have:\r<BR>\n" );
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document.write( "(20 - x) / x  (ratio of 2nd term to 1st term)\r<BR>\n" );
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document.write( "(-5/8 - y) / y (ratio of 7th term to 6th term)\r<BR>\n" );
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document.write( "I set the equal to each other because the ratios are required to be the same in a GP:\r<BR>\n" );
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document.write( "(20 - x) / x = (-5/8 - y) / y\r<BR>\n" );
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document.write( "20y - xy = (-5/8)x - xy<BR>\n" );
document.write( "20y = (-5/8)x<BR>\n" );
document.write( "  y = (-1/32)x\r<BR>\n" );
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document.write( "OR solving the same equation for x gives:  x = -32y\r<BR>\n" );
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document.write( "From this point I thought about trying to just choose numbers either for x or y and then use the given common ratio to find the rest of the terms, but it didn't work out.  Can you provide me with a step-by-step solution to this intriguing question?  Thank you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287779 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=287779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maybe if you make use of the fact<BR>\n" );
document.write( "that the 1st term is a, the 2nd term is ar<BR>\n" );
document.write( "the 6th term is ar^5 and the 7th term<BR>\n" );
document.write( "is ar^6, you can get a new relation of<BR>\n" );
document.write( "x to y.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=========== </SPAN>\n" );
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