document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912611>Question 912611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Enter the 12th term of the sequence for each whole number greater than 1.\r<BR>\n" );
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document.write( "f(1) = 1 and f(n) = 2 · f(n &#8722; 1)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553923 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=553923\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(1) = 1 and f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "The idea is to find f(12). We can't do this directly since we're given this recursive sequence. We need to know f(1), f(2), ..., f(10), f(11) before we can determine f(12).\r<BR>\n" );
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document.write( "So plug in n = 2, n = 3, etc into f(n) = 2*f(n-1) to find f(2), ..., f(10), f(11)\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(2) = 2*f(2-1)\r<BR>\n" );
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document.write( "f(2) = 2*f(1)\r<BR>\n" );
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document.write( "f(2) = 2*1\r<BR>\n" );
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document.write( "f(2) = 2\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(3) = 2*f(3-1)\r<BR>\n" );
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document.write( "f(3) = 2*f(2)\r<BR>\n" );
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document.write( "f(3) = 2*2\r<BR>\n" );
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document.write( "f(3) = 4\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(4) = 2*f(4-1)\r<BR>\n" );
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document.write( "f(4) = 2*f(3)\r<BR>\n" );
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document.write( "f(4) = 2*4\r<BR>\n" );
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document.write( "f(4) = 8\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(5) = 2*f(5-1)\r<BR>\n" );
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document.write( "f(5) = 2*f(4)\r<BR>\n" );
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document.write( "f(5) = 2*8\r<BR>\n" );
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document.write( "f(5) = 16\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(6) = 2*f(6-1)\r<BR>\n" );
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document.write( "f(6) = 2*f(5)\r<BR>\n" );
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document.write( "f(6) = 2*16\r<BR>\n" );
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document.write( "f(6) = 32\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(7) = 2*f(7-1)\r<BR>\n" );
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document.write( "f(7) = 2*f(6)\r<BR>\n" );
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document.write( "f(7) = 2*32\r<BR>\n" );
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document.write( "f(7) = 64\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(8) = 2*f(8-1)\r<BR>\n" );
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document.write( "f(8) = 2*f(7)\r<BR>\n" );
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document.write( "f(8) = 2*64\r<BR>\n" );
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document.write( "f(8) = 128\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(9) = 2*f(9-1)\r<BR>\n" );
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document.write( "f(9) = 2*f(8)\r<BR>\n" );
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document.write( "f(9) = 2*128\r<BR>\n" );
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document.write( "f(9) = 256\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(10) = 2*f(10-1)\r<BR>\n" );
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document.write( "f(10) = 2*f(9)\r<BR>\n" );
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document.write( "f(10) = 2*256\r<BR>\n" );
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document.write( "f(10) = 512\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(11) = 2*f(11-1)\r<BR>\n" );
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document.write( "f(11) = 2*f(10)\r<BR>\n" );
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document.write( "f(11) = 2*512\r<BR>\n" );
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document.write( "f(11) = 1024\r<BR>\n" );
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document.write( "f(n) = 2*f(n-1)\r<BR>\n" );
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document.write( "f(12) = 2*f(12-1)\r<BR>\n" );
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document.write( "f(12) = 2*f(11)\r<BR>\n" );
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document.write( "f(12) = 2*1024\r<BR>\n" );
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document.write( "f(12) = 2048\r<BR>\n" );
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document.write( "The first twelve terms are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048\r<BR>\n" );
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document.write( "The 12th term is <font color=\"red\">2048</font> which is the final answer\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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