document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212918>Question 212918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is: Three consecutive terms of a geometric sequence have a sum of 28 and a product of 512. Find these numbers.<BR>\n" );
document.write( "(Hint: let these numbers be a/r, a and ar )\r<BR>\n" );
document.write( "\n" );
document.write( "I really don't understand the question, anyone kindly help me??\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160851 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A geometric sequence looks like:<BR>\n" );
document.write( "7<BR>\n" );
document.write( "7*3 = 21<BR>\n" );
document.write( "21*3 = 63<BR>\n" );
document.write( "63*3 = 189<BR>\n" );
document.write( "108*3 = 567<BR>\n" );
document.write( "The sequence is:<BR>\n" );
document.write( "7,21,63,189,567<BR>\n" );
document.write( "In the general formula, I call the nth term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+7 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+21 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "The multiplier for each term, in this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "is called <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+a%5Bn%2B1%5D%2Fa%5Bn%5D ALIGN=MIDDLE  ALT=\"r+=+a%5Bn%2B1%5D%2Fa%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All this is saying is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324%2F108+=+3 ALIGN=MIDDLE  ALT=\"324%2F108+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F36+=+3 ALIGN=MIDDLE  ALT=\"108%2F36+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F21+=+3 ALIGN=MIDDLE  ALT=\"36%2F21+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F7+=+3 ALIGN=MIDDLE  ALT=\"21%2F7+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Another general formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Testing the formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+a%5B1%5D%2A3%5E0 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+a%5B1%5D%2A3%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%5B1%5D%2A3%5E1 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5D%2A3%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+a%5B1%5D%2A3%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%5B1%5D%2A3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+a%5B1%5D%2A3%5E3 ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%5B1%5D%2A3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D+=+a%5B1%5D%2A3%5E4 ALIGN=MIDDLE  ALT=\"a%5B5%5D+=+a%5B1%5D%2A3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+7 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then I get<BR>\n" );
document.write( "7,21,63,189,567<BR>\n" );
document.write( "Now, refering back to your problem, they are just saying<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+a ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, using my formula again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+a%2Ar%5E0 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+a%2Ar%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%2Ar%5E1 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%2Ar%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+a%2Ar%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D+=+a%2Ar%5E3 ALIGN=MIDDLE  ALT=\"a%5B4%5D+=+a%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D+=+a%2Ar%5E4 ALIGN=MIDDLE  ALT=\"a%5B5%5D+=+a%2Ar%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sequence is:<BR>\n" );
document.write( "a, ar, ar^2, ar^3, ar^4<BR>\n" );
document.write( "By suggesting that you use a/r, a, and ar, what<BR>\n" );
document.write( "they are doing is starting the sequence with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D ALIGN=MIDDLE  ALT=\"a%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which still gives you a valid sequence<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D+=+a%2Ar%5E%28-1%29 ALIGN=MIDDLE  ALT=\"a%5B0%5D+=+a%2Ar%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+a%2Ar%5E0 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+a%2Ar%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%2Ar%5E1 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%2Ar%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+a%2Ar%5E2 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+a%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sequence is<BR>\n" );
document.write( "a/r, a, ar, ar^2<BR>\n" );
document.write( "Using my example with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+3 ALIGN=MIDDLE  ALT=\"r+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "the terms would be:<BR>\n" );
document.write( "7/3, 7, 21, 63, etc, which is still valid<BR>\n" );
document.write( "Three consecutive terms of a geometric sequence have a sum of 28 and a product of 512, so<BR>\n" );
document.write( "(1)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fr+%2B+a+%2B+ar+=+28 ALIGN=MIDDLE  ALT=\"a%2Fr+%2B+a+%2B+ar+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fr%29%2Aa%2Aar+=+512 ALIGN=MIDDLE  ALT=\"%28a%2Fr%29%2Aa%2Aar+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+512 ALIGN=MIDDLE  ALT=\"a%5E3+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+8 ALIGN=MIDDLE  ALT=\"a+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plugging this into the 1st equation,<BR>\n" );
document.write( "(1)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fr+%2B+8+%2B+8r+=+28 ALIGN=MIDDLE  ALT=\"8%2Fr+%2B+8+%2B+8r+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+%2B+8r+%2B+8r%5E2+=+28 ALIGN=MIDDLE  ALT=\"8+%2B+8r+%2B+8r%5E2+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2B+2r+%2B+2r%5E2+=+7 ALIGN=MIDDLE  ALT=\"2+%2B+2r+%2B+2r%5E2+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%5E2+%2B+2r+-+5+=+0 ALIGN=MIDDLE  ALT=\"2r%5E2+%2B+2r+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formua:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2 ALIGN=MIDDLE  ALT=\"b+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-5 ALIGN=MIDDLE  ALT=\"c+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );