document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=639363>Question 639363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for the next two numbers in the following number sequence: 1728, 1000, 512, 216, _, _. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402710 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=402710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each number is a perfect cube. Notice how 12^3 = 1728, 1000 = 10^3, 512 = 8^3, 216 = 6^3\r<BR>\n" );
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document.write( "So the form is n^3 where 'n' is some integer. But we're only focusing on positive even integers and we're counting down to the next even integer each time. Moreover, we're starting at 12. So 'n' becomes -2n+12 where n starts at n = 0. If you want to start at n = 1, then you have to add 2 to 12 to get -2n+14\r<BR>\n" );
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document.write( "So the sequence follows the form (-2n+14)^3 where n is a positive integer and n starts at n = 1\r<BR>\n" );
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document.write( "We can see that when n = 1, (-2n+14)^3 = (-2*1+14)^3 = 1728\r<BR>\n" );
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document.write( "When n = 2, (-2n+14)^3 = (-2*2+14)^3 = 1000\r<BR>\n" );
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document.write( "etc etc\r<BR>\n" );
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document.write( "all the way up to n = 4, (-2n+14)^3 = (-2*4+14)^3 = 216\r<BR>\n" );
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document.write( "The next two terms are \r<BR>\n" );
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document.write( "n = 5, (-2n+14)^3 = (-2*5+14)^3 = 64\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "n = 6, (-2n+14)^3 = (-2*6+14)^3 = 8\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the updated sequence is\r<BR>\n" );
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document.write( "1728, 1000, 512, 216, _<u><font color=\"red\">64</font></u>_, _<u><font color=\"red\">8</font></u>_ </SPAN>\n" );
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