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 #120876 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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=120876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 1st term has 2 Bs and 2 As<BR>\n" );
document.write( "the 2nd term has 3 Bs and 4 As<BR>\n" );
document.write( "the 3rd term has 4 Bs and 6 As<BR>\n" );
document.write( "the 4th term has 5 Bs and 8 As\r<BR>\n" );
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document.write( "so the nth term has (n + 1) Bs and 2n As\r<BR>\n" );
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document.write( "to find the term which has exactly 35% Bs:<BR>\n" );
document.write( "(n + 1) = 35/100 * (2n + (n + 1))<BR>\n" );
document.write( "<=> n + 1 = 0.35*(3n + 1)<BR>\n" );
document.write( "<=> n + 1 = 1.05n + 0.35<BR>\n" );
document.write( "<=> n - 1.05n = 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( "so the 13th term has exactly 35% Bs<BR>\n" );
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