document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658798>Question 658798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A theatre has 49 seats, 53 in the second row, 57 seats in the third row and so on.\r<BR>\n" );
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document.write( "a.  can the number of seats in each row be numbered in geometric or arithmetic sequence?\r<BR>\n" );
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document.write( "b. write the general term for a sequence a[n] that gives the number of seats in row n.    a[n]=\r<BR>\n" );
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document.write( "c. how many seats are in row 18? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410524 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> row 1 = 49<BR>\n" );
document.write( "row 2 = 53<BR>\n" );
document.write( "row 3 = 57<BR>\n" );
document.write( "this is an arithmetic sequence<BR>\n" );
document.write( "formula for the last term in an arithmetic sequence is l = a + (n-1)d<BR>\n" );
document.write( "a is the first number in the sequence<BR>\n" );
document.write( "l is the last number in the sequence<BR>\n" );
document.write( "n is the number of terms in the sequence.<BR>\n" );
document.write( "for the part of the sequence that is given to you, we get:<BR>\n" );
document.write( "a = 49<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "d = 4<BR>\n" );
document.write( "use this formula to find the number of the last term in the sequence.<BR>\n" );
document.write( "you get l = 49 + 2*4 = 49 + 8 = 57<BR>\n" );
document.write( "as you can see, the last term in the sequence is 57 as given so the formula is good.<BR>\n" );
document.write( "we know it's an arithmetic sequence because it has a common difference which is 4.<BR>\n" );
document.write( "the number of seats in row 18 would be given by the same formula.<BR>\n" );
document.write( "l = a + (n-1) * d which becomes l = 49 + 17*4 which becomes l = 49 + 68 which becomes l = 117<BR>\n" );
document.write( "if you wanted to take the trouble of actually plotting out the sequence, it would look like this:<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "i       x.i\r\n" );
document.write( "1	49\r\n" );
document.write( "2	53\r\n" );
document.write( "3	57\r\n" );
document.write( "4	61\r\n" );
document.write( "5	65\r\n" );
document.write( "6	69\r\n" );
document.write( "7	73\r\n" );
document.write( "8	77\r\n" );
document.write( "9	81\r\n" );
document.write( "10	85\r\n" );
document.write( "11	89\r\n" );
document.write( "12	93\r\n" );
document.write( "13	97\r\n" );
document.write( "14	101\r\n" );
document.write( "15	105\r\n" );
document.write( "16	109\r\n" );
document.write( "17	113\r\n" );
document.write( "18	117\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "i is the row number<BR>\n" );
document.write( "x.i is the number of seats in that row.\r<BR>\n" );
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document.write( "this is not a geometric sequence because you don't have a common ratio.<BR>\n" );
document.write( "the formula for a geometric sequence is l = a*r^(n-1)<BR>\n" );
document.write( "an example of a geometric sequence would be:<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "4<BR>\n" );
document.write( "8<BR>\n" );
document.write( "the common ratio is 2 because each number is 2 times the number before it.<BR>\n" );
document.write( "in this geometric sequence, the 4th number in the sequence would be found using the formula of l = 1*2^3 which becomes l = 1*8 which becomes l = 8.<BR>\n" );
document.write( "since the 4th number in the sequence is 8, the formula works.\r<BR>\n" );
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document.write( "in your problem there is no common ratio.\r<BR>\n" );
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document.write( "53/49 = 1.0816326...<BR>\n" );
document.write( "57/53 = 1.0754716...\r<BR>\n" );
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document.write( "there is, however, a common difference of 4.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );