document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197145>Question 1197145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An auditorium has 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on, and 30 rows of seats. How many seats are in the theatre? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830268 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=830268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is an arithmetic sequence because we increase each term by the same amount each time.<BR>\n" );
document.write( "a1 = 20 = first term<BR>\n" );
document.write( "d = 4 = common difference\r<BR>\n" );
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document.write( "an = nth term<BR>\n" );
document.write( "an = a1 + d(n-1)<BR>\n" );
document.write( "an = 20 + 4(n-1)\r<BR>\n" );
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document.write( "Plug in n = 30 to find how many seats are in the 30th row<BR>\n" );
document.write( "an = 20 + 4(n-1)<BR>\n" );
document.write( "a30 = 20 + 4(30-1)<BR>\n" );
document.write( "a30 = 136<BR>\n" );
document.write( "There are 136 seats in the 30th row.\r<BR>\n" );
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document.write( "Now use this formula to find the sum of the first n terms of an arithmetic sequence.<BR>\n" );
document.write( "Sn = sum of the first n terms<BR>\n" );
document.write( "Sn = (n/2)*(firstTerm + nthTerm)<BR>\n" );
document.write( "Sn = (n/2)*(a1 + an)<BR>\n" );
document.write( "S30 = (30/2)*(a1 + a30)<BR>\n" );
document.write( "S30 = 15*(20 + 136)<BR>\n" );
document.write( "S30 = 2340<BR>\n" );
document.write( "The first 30 terms of the arithmetic sequence {20,24,28,...} add to 2340.<BR>\n" );
document.write( "Therefore, we have 2340 total seats.\r<BR>\n" );
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document.write( "To verify this, you can use a spreadsheet to generate the first 30 terms. <BR>\n" );
document.write( "Type 20 into cell A1. Type 24 into cell A2. Then select cells A1 and A2. \r<BR>\n" );
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document.write( "While selected, there should be a small square black box at the bottom right corner of cell A2. When you highlight your mouse over this tiny black square, the mouse cursor should turn into a plus sign. <BR>\n" );
document.write( "Drag this symbol down until you have generated all 30 terms needed. You should see the sequence 20,24,28,...,132,136 for cells A1 through A30 respectively.\r<BR>\n" );
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document.write( "Alternatively, you can use the \"fill series\" command to generate the 30 terms needed.\r<BR>\n" );
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document.write( "In cell B1, type in <font color=blue>=SUM(A1:A30)</font> to quickly add up all the terms rather than manually typing them in. The result of this command is 2340.\r<BR>\n" );
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document.write( "Answer: 2340 seats total<BR>\n" );
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