document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163802>Question 1163802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hours before tickets for a rock concert were to<BR>\n" );
document.write( "go on sale, people were lined up to buy tickets.<BR>\n" );
document.write( "In fact, the first person came 12 hours before<BR>\n" );
document.write( "the ticket booth was to open. A new group of<BR>\n" );
document.write( "ticket buyers joined the line every 30 minutes.\r<BR>\n" );
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document.write( "a. If each new group has two persons more than<BR>\n" );
document.write( "the previous group, how many people were <BR>\n" );
document.write( "in line after the 20th group joined?\r<BR>\n" );
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document.write( "b. How many people were in line 3 hours<BR>\n" );
document.write( "before the ticket booth opened?\r<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 #788055 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of people in each group can be represented by an arithmetic progression, with the first term equal to 1 <BR>\n" );
document.write( "and the common difference equal to 2.<BR>\n" );
document.write( "The nth term of the progression is: a_n = 1 + 2(n-1)<BR>\n" );
document.write( "Thus in the 20th group, there are a_20 = 1 + 2(19) = 39 people<BR>\n" );
document.write( "The total number of people is the cumulative sum which is given by:<BR>\n" );
document.write( "S_n = (n/2)*(a_1 + a_n) -> S_20 = 10*(1 + 39) = 400<BR>\n" );
document.write( "3 hours before, there are a total of 2*9 = 18 groups in line<BR>\n" );
document.write( "S_18 = 9*(1+35) = 324 </SPAN>\n" );
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