document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088941>Question 1088941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you ikleyn for solving my question about the theater problem.\r<BR>\n" );
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document.write( "The sum of the the first nine terms of an arithmetic sequence is 99, and its seventh term is 19. What is its ninth term?\r<BR>\n" );
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document.write( "So far my solution is(Im unsure of my solution)<BR>\n" );
document.write( "a7=19(Seventh term);a9=99(First nine terms); a9=?(Ninth term)\r<BR>\n" );
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document.write( "Sn=n/2(a1+an)<BR>\n" );
document.write( "Sn=9/2(a1+a9)<BR>\n" );
document.write( "99=4.5(a1 + ______) [Not sure what to add here]\r<BR>\n" );
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document.write( "a9=a6+a7+6d<BR>\n" );
document.write( "a9=a7+19+6d<BR>\n" );
document.write( "a9=a1+7d+19+6d<BR>\n" );
document.write( "a9=a1+19+13d<BR>\n" );
document.write( "2a1+19+13d\r<BR>\n" );
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document.write( "Basically I am not sure of my formula. If you don't seem to understand the problem, I have a sample problem(with solution) identical to this problem you can request it if you want. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703265 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=703265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formulas for arithmetic sereis are:\r<BR>\n" );
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document.write( "An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "Sn = n * (A1 + An) / 2\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "A7 = 19\r<BR>\n" );
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document.write( "S9 = 99\r<BR>\n" );
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document.write( "from An = A1 + (n-1) * d, you derive:\r<BR>\n" );
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document.write( "A7 = A1 + 6d\r<BR>\n" );
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document.write( "since A7 = 19, you derive:\r<BR>\n" );
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document.write( "19 = A1 + 6d\r<BR>\n" );
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document.write( "from that, you derive:\r<BR>\n" );
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document.write( "A1 = 19 - 6d\r<BR>\n" );
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document.write( "using the same formula of An = A1 + (n-1) * d, you derive:\r<BR>\n" );
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document.write( "A9 = A1 + 8d\r<BR>\n" );
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document.write( "you know that A7 = A1 + 6d\r<BR>\n" );
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document.write( "if you subtract A7 from A9, you (A1 + 6d) subtract from (A1 + 8d) which gets you:\r<BR>\n" );
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document.write( "A9 minus A7 = (A1 + 8d) minus (A1 + 6d) = A1 + 8d - A1 - 6d = 2d\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "A9 minus A7 = 2d\r<BR>\n" );
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document.write( "solve for A9 to get A9 = A7 + 2d\r<BR>\n" );
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document.write( "since you know A7 is equal to 19, then you get:\r<BR>\n" );
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document.write( "A9 = 19 + 2d\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "A1 = 19 - 6d\r<BR>\n" );
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document.write( "A9 = 19 + 2d\r<BR>\n" );
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document.write( "the formula for Sn = n * (A1 + An) / 2\r<BR>\n" );
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document.write( "when n = 9, this formula becomes S9 = 9 * (A1 + A9) / 2\r<BR>\n" );
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document.write( "you know that S9 = 99 and you derived that A1 = 19 - 6d and A9 = 19 + 2d. \r<BR>\n" );
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document.write( "your formula of S9 = 9 * (A1 + A9) / 2 becomes:\r<BR>\n" );
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document.write( "99 = 9 * ((19-6d) + (19+2d)) / 2\r<BR>\n" );
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document.write( "simplify this formula to get:\r<BR>\n" );
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document.write( "99 = 9 * (38 - 4d) / 2\r<BR>\n" );
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document.write( "multiply both sides of this formula by 2 to get:\r<BR>\n" );
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document.write( "198 = 9 * (38 - 4d)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "198 = 342 - 36d\r<BR>\n" );
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document.write( "solve for d to get:\r<BR>\n" );
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document.write( "d = (342 - 198) / 36\r<BR>\n" );
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document.write( "this results in d = 4\r<BR>\n" );
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document.write( "now that you know that d = 4, you can solve for A1 and A9.\r<BR>\n" );
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document.write( "A1 = 19 - 6d = 19 - 6*4 = 19 - 24 = -5\r<BR>\n" );
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document.write( "A9 = 19 + 2*d = 19 + 8 = 27\r<BR>\n" );
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document.write( "you have A1 = -5 and A9 = 27\r<BR>\n" );
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document.write( "the formula for Sn is Sn = n * (A1 + An) / 2\r<BR>\n" );
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document.write( "this becomes S9 = 9 * (-5 + 27) / 2\r<BR>\n" );
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document.write( "solve for S9 = 9 * 22 / 2 = 9 * 11 = 99 which is what is should be.\r<BR>\n" );
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document.write( "your solution is that the 9th term is 27.\r<BR>\n" );
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document.write( "your sequence from first term to 9th term is:\r<BR>\n" );
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document.write( "-5 = first term<BR>\n" );
document.write( "-1 = second<BR>\n" );
document.write( "3 = third<BR>\n" );
document.write( "7 = fourth<BR>\n" );
document.write( "11 = fifth<BR>\n" );
document.write( "15 = sixth<BR>\n" );
document.write( "19 = seventh *****<BR>\n" );
document.write( "23 = eighth<BR>\n" );
document.write( "27 = ninth *****\r<BR>\n" );
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document.write( "sum of all 9 terms is 99\r<BR>\n" );
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document.write( "everything check out so the solution looks good.\r<BR>\n" );
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document.write( "the ninth term is 27.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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