document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=777509>Question 777509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A playground is being designed where children can interact with their friends in certain combinations. <BR>\n" );
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. <BR>\n" );
document.write( "Which recursive equation represents the pattern?\r<BR>\n" );
document.write( "\n" );
document.write( "a. an = an - 1 + 2(n - 1) \r<BR>\n" );
document.write( "\n" );
document.write( "b. an = an - 1 + (n - 1) 2 \r<BR>\n" );
document.write( "\n" );
document.write( "c. an = an - 1 + 2(n - 1) \r<BR>\n" );
document.write( "\n" );
document.write( "d. an = an - 1 + (2n - 1) \r<BR>\n" );
document.write( "\n" );
document.write( "I want to know the proccess on how to do this not only the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #474123 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=474123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A playground is being designed where children can interact with their friends in certain combinations. <BR>\n" );
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. <BR>\n" );
document.write( "Which recursive equation represents the pattern?<BR>\n" );
document.write( "Note: There is no magic to finding the answer.  You just have<BR>\n" );
document.write( "to test each one to see what does and what does not give the answer.<BR>\n" );
document.write( "------------------------------ <BR>\n" );
document.write( "a. an = a(n - 1) + 2(n - 1)<BR>\n" );
document.write( "a1 = 0 + 2*0<BR>\n" );
document.write( "a2 = 0 + 2*1 = 2 fails at a2<BR>\n" );
document.write( "-------------------------------------- <BR>\n" );
document.write( "b. an = a(n - 1) + (n - 1)^2<BR>\n" );
document.write( "a1 = 0 + 0^2 = 0<BR>\n" );
document.write( "a2 = 0 + 1^2 = 1<BR>\n" );
document.write( "a3 = 1 + 2^2 = 5<BR>\n" );
document.write( "a4 = 3 + 3^2 = 12 fails at a4<BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "etc...<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( "c. an = a(n - 1) + 2(n - 1) <BR>\n" );
document.write( "d. an = a(n - 1) + (2n - 1) <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );