document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495959>Question 495959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. I would appreciate an explanation to the following question:\r<BR>\n" );
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document.write( "A playground is being designed where children can interact with their friends in certain combinations.\r<BR>\n" );
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document.write( "If there is 1 child, there can be 0 interactions.<BR>\n" );
document.write( "If there are 2 children, there can be only 1 interaction.<BR>\n" );
document.write( "If there are 3 children , there can be 5 interactions. <BR>\n" );
document.write( "If there are 4 children, there can be 14 interactions. \r<BR>\n" );
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document.write( "Which recursive pattern represents the pattern?<BR>\n" );
document.write( "asubn=asubn-1+2^(n-1)<BR>\n" );
document.write( "asubn=asubn+(n-1)^2<BR>\n" );
document.write( "asubn=asubn+2(n-1)<BR>\n" );
document.write( "asubn=asubn+(2n-1)\r<BR>\n" );
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document.write( "So far I have figured out by setting up this basic pattern chart that:<BR>\n" );
document.write( "                               <BR>\n" );
document.write( "n  a   <BR>\n" );
document.write( "1  0   +1       <BR>\n" );
document.write( "2  1   +4         <BR>\n" );
document.write( "3  5   +9<BR>\n" );
document.write( "4  14<BR>\n" );
document.write( "Is the equation always the same? or does it change with the given information. I got this wrong and would appreciate understanding why? I understand how to make derive the sequence information. What if I need the 50th term? I can easily get the ninth term as in the previous question on this assignment. But having trouble understanding how to write the formula. \r<BR>\n" );
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document.write( "I appreciate you help. This is a wonderful resource for students who take math seriously because the tutors answer the questions so thoroughly. Again, thank you in advance. \r<BR>\n" );
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document.write( "Justina    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336294 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=336294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula that works with the data is as follows:\r<BR>\n" );
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document.write( "a[n] = a[n-1] + (n-1)^2\r<BR>\n" );
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document.write( "here's a table of values based on that formula.<BR>\n" );
document.write( "the table starts with a[1] being given as 0.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "        n        (n-1)^2         a[n]\r\n" );
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document.write( "        1        n/a            given as 0\r\n" );
document.write( "        2        1^2 = 1        1 + 0 = 1\r\n" );
document.write( "        3        2^2 = 4        4 + 1 = 5\r\n" );
document.write( "        4        3^2 = 9        9 + 5 = 14\r\n" );
document.write( "        5        4^2 = 16       16 + 14 = 30\r\n" );
document.write( "        6        5^2 = 25       25 + 30 = 55\r\n" );
document.write( "        ...\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "you are given that the a[1] = 0<BR>\n" );
document.write( "the rest of them are derived from the formula.<BR>\n" );
document.write( "the same formula is used every time.<BR>\n" );
document.write( "let me know if this solves the problem for you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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