document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164033>Question 164033</A>: <I><SPAN STYLE=\"word-break: break-all;\">     The first four terms of a pattern are shown below: \r<BR>\n" );
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document.write( "ABBA<BR>\n" );
document.write( "AABBBAA<BR>\n" );
document.write( "AAABBBBAAA<BR>\n" );
document.write( "AAAABBBBBAAAA \r<BR>\n" );
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document.write( "Suppose that this pattern continues, with the As and Bs increasing as shown. \r<BR>\n" );
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document.write( "Find an expression for the number of Bs in the nth term of the pattern.\r<BR>\n" );
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document.write( "Use your expression to determine which term has exactly 35% Bs.<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 #120875 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "(Please show source)<BR>\n" );
document.write( ".................n<BR>\n" );
document.write( "ABBA.............1     2 Bs    2 As<BR>\n" );
document.write( "AABBBAA..........2     3 Bs    4 As<BR>\n" );
document.write( "AAABBBBAAA.......3     4 Bs    6 As<BR>\n" );
document.write( "AAAABBBBBAAAA....4     5 Bs    8 As<BR>\n" );
document.write( "........\r<BR>\n" );
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document.write( "AAA,,,BBB,,,,AAA.n    n+1 Bs   2n As\r<BR>\n" );
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document.write( "Answer: Number of Bs in the nth term is n+1\r<BR>\n" );
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document.write( "we have to find n such that <BR>\n" );
document.write( " Bs/Total =0.35<BR>\n" );
document.write( "then\r<BR>\n" );
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document.write( "(n+1)/(n+1+2n)=0.35<BR>\n" );
document.write( "n+1=0.35(3n+1)\r<BR>\n" );
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document.write( "n-(1.05)n=0.35-1<BR>\n" );
document.write( "-0.05n=-0.65<BR>\n" );
document.write( "n=0.65/0.05=13\r<BR>\n" );
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document.write( "Answer: n=13<BR>\n" );
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