document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=439410>Question 439410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of three consecutive terms in a geometric sequence is -1000, and their sum is 15. Find 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 #303669 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=303669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a, ar, and <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;\" > be the terms in geometric sequence.\r<BR>\n" );
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document.write( "Then from the given, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Aar%2Aar%5E2+=+a%5E3r%5E3+=+%28ar%29%5E3+=+-1000 ALIGN=MIDDLE  ALT=\"a%2Aar%2Aar%5E2+=+a%5E3r%5E3+=+%28ar%29%5E3+=+-1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or ar = -10, after taking cube roots. <BR>\n" );
document.write( "==> a = -10/r.<BR>\n" );
document.write( "Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+ar+%2B+ar%5E2+=+15 ALIGN=MIDDLE  ALT=\"a+%2B+ar+%2B+ar%5E2+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%2Br%2Br%5E2%29+=+15 ALIGN=MIDDLE  ALT=\"a%281%2Br%2Br%5E2%29+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%2Fr%29%281%2Br%2Br%5E2%29+=+15 ALIGN=MIDDLE  ALT=\"%28-10%2Fr%29%281%2Br%2Br%5E2%29+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+r%5E2+%2B+5r+%2B+2 ALIGN=MIDDLE  ALT=\"0+=+r%5E2+%2B+5r+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after cross-multiplying and simplifying.<BR>\n" );
document.write( "<==> (2r+1)(r+1) = 0<BR>\n" );
document.write( "==> r = -1/2 or -2<BR>\n" );
document.write( "==> a = 20 or 5, respectively.<BR>\n" );
document.write( "Hence the sequences are {20, -10, 5} and { 5, -10, 20}.  (The two sequences are DIFFERENT because they have different first terms and common ratios.) </SPAN>\n" );
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