document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197143>Question 1197143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An audio-visual room (AVR) at Adamson University has 7 seats on the first row, 10 on the second row, 13 on the third row, and so on, and 40 rows of seats. How many seats are in the AVR?  </SPAN>\n" );
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document.write( "Please see this similar question before reading onward<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1197145.html\">https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1197145.html</a><BR>\n" );
document.write( "This similar question may help you solve the problem on your own. <BR>\n" );
document.write( "If you still need help, then the solution is in the next section below.\r<BR>\n" );
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document.write( "We have an arithmetic sequence since the gap between terms is the same.<BR>\n" );
document.write( "10-7 = 3<BR>\n" );
document.write( "13-10 = 3<BR>\n" );
document.write( "Each time we get to a new row, we add on 3 seats.<BR>\n" );
document.write( "This is the common difference.<BR>\n" );
document.write( "d = common difference = 3\r<BR>\n" );
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document.write( "The first term is a1 = 7\r<BR>\n" );
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document.write( "Summary so far<BR>\n" );
document.write( "a1 = 7<BR>\n" );
document.write( "d = 3\r<BR>\n" );
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document.write( "Let's form the nth term of the arithmetic sequence<BR>\n" );
document.write( "an = a1 + d(n-1)<BR>\n" );
document.write( "an = 7 + 3(n-1)\r<BR>\n" );
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document.write( "As a check, let's plug in n = 2 and we should get 10 seats<BR>\n" );
document.write( "an = 7 + 3(n-1)<BR>\n" );
document.write( "a2 = 7 + 3(2-1)<BR>\n" );
document.write( "a2 = 10<BR>\n" );
document.write( "That works out. I'll let you verify other values of n.\r<BR>\n" );
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document.write( "Now plug in n = 40<BR>\n" );
document.write( "an = 7 + 3(n-1)<BR>\n" );
document.write( "a40 = 7 + 3(40-1)<BR>\n" );
document.write( "a40 = 124<BR>\n" );
document.write( "There are 124 seats in row 40.\r<BR>\n" );
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document.write( "Now apply this summation formula<BR>\n" );
document.write( "Sn = sum of the first n terms of an arithmetic sequence<BR>\n" );
document.write( "Sn = (n/2)*(firstTerm + nthTerm) <BR>\n" );
document.write( "S40 = (40/2)*(firstTerm + 40thTerm) <BR>\n" );
document.write( "S40 = 20*(7 + 124)<BR>\n" );
document.write( "S40 = 2620\r<BR>\n" );
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document.write( "An alternative formula is this<BR>\n" );
document.write( "Sn = (n/2)*(2*a1 + d(n-1))<BR>\n" );
document.write( "S40 = (40/2)*(2*7 + 3*(40-1))<BR>\n" );
document.write( "S40 = 2620\r<BR>\n" );
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document.write( "The verification process is similar to that shown in the link above.\r<BR>\n" );
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document.write( "Answer: <font color=red>2620</font> seats total<BR>\n" );
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