document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190567>Question 1190567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help: the sum of the first two terms of a G.P is x.The sum of the last two is 1 if there are n term in all, calculate the common ratio  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822264 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "r = common ratio\r<BR>\n" );
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document.write( "Let's ignore the first two terms.\r<BR>\n" );
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document.write( "The last two terms of the geometric progression (GP), aka geometric sequence, sum to 1.<BR>\n" );
document.write( "a = second to last term<BR>\n" );
document.write( "ar = last term\r<BR>\n" );
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document.write( "a+ar = 1<BR>\n" );
document.write( "ar = 1-a<BR>\n" );
document.write( "r = (1-a)/a\r<BR>\n" );
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document.write( "If we had <BR>\n" );
document.write( "a = 0.2<BR>\n" );
document.write( "for instance, then it would mean,<BR>\n" );
document.write( "r = (1-a)/a = (1-0.2)/0.2 = 0.8/0.2 = 4<BR>\n" );
document.write( "ar = 0.2*4 = 0.8<BR>\n" );
document.write( "a+ar = 0.2 + 0.8 = 1\r<BR>\n" );
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document.write( "Or we could have<BR>\n" );
document.write( "a = 0.4<BR>\n" );
document.write( "for instance, then it would mean<BR>\n" );
document.write( "r = (1-a)/a = (1-0.4)/0.4 = 0.6/0.4 = 1.5<BR>\n" );
document.write( "ar = 0.4*1.5 = 0.6<BR>\n" );
document.write( "a+ar = 0.4 + 0.6 = 1\r<BR>\n" );
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document.write( "As you can see, these are two examples of having two terms of a geometric sequence add to 1. <BR>\n" );
document.write( "It turns out there are infinitely many ways to do this.\r<BR>\n" );
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document.write( "It doesn't matter what those two original first terms sum to (ie. it doesn't matter what x is)<BR>\n" );
document.write( "The problem is effectively the same as asking \"the sum of the first two terms of a GP is 1. What is the common ratio?\"\r<BR>\n" );
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document.write( "In short, there are infinitely many possible solutions here. There isn't enough info to answer this current question.<BR>\n" );
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