document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047092>Question 1047092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi I am learning pre-calculus 11 and am stuck on this question thank you! \r<BR>\n" );
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document.write( "Q. Determine the sum, Sn, for each arithmetic sequence described.<BR>\n" );
document.write( "a) T1=7, Tn=79, n=8 \r<BR>\n" );
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document.write( "they do not tell me what D is, so I am confused.. :)<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 #662568 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=662568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> these are the formulas for an arithmetic sequence that i know.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm</a>\r<BR>\n" );
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document.write( "they should be the same as your formulas, except they use a rather than T and d rather than D.\r<BR>\n" );
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document.write( "converting their formulas to your nomenclature, i get:\r<BR>\n" );
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document.write( "Tn = T1 + (n-1) * D\r<BR>\n" );
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document.write( "Sn = n * (T1 + Tn) / 2\r<BR>\n" );
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document.write( "from the formulas and from what you are given, you don't need to find D, but i'll show you how to find it anyway after solving the problem.\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "a) T1=7, Tn=79, n=8 \r<BR>\n" );
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document.write( "the formula for the sum of an arithmetic sequence is:\r<BR>\n" );
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document.write( "Sn = n * (T1 + Tn) / 2\r<BR>\n" );
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document.write( "you have what you need.\r<BR>\n" );
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document.write( "replace T1 with 7 and Tn with 79 and n with 8 and you have:\r<BR>\n" );
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document.write( "S8 = 8 * (7 + 79) / 2\r<BR>\n" );
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document.write( "solve for S8 to get S8 = 344\r<BR>\n" );
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document.write( "you didn't need D if you used the Sn formula.\r<BR>\n" );
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document.write( "you could solve for D as follows:\r<BR>\n" );
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document.write( "the formula for Tn is:\r<BR>\n" );
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document.write( "Tn = T1 + (n-1) * D\r<BR>\n" );
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document.write( "replace Tn with 79 and T1 with 7 and n with 8 and you get:\r<BR>\n" );
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document.write( "79 = 7 + (8-1) * D\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "79 = 7 + 7 * D\r<BR>\n" );
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document.write( "subtract 7 from both sides of the equation to get:\r<BR>\n" );
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document.write( "72 = 7 * D\r<BR>\n" );
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document.write( "solve for D to get:\r<BR>\n" );
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document.write( "D = 72/7.\r<BR>\n" );
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document.write( "your formula of Tn = T1 + (n-1) * D becomes T8 = 7 + 7 * 72/7\r<BR>\n" );
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document.write( "solve for T8 to get T8 = 79.\r<BR>\n" );
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document.write( "value of D looks good.\r<BR>\n" );
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document.write( "you can also calculate each term from 1 to 8 and then add them up to see if the formula work as advertised.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "T1 = 7 = 49/7<BR>\n" );
document.write( "T2 = 7 + 1 * 72/7 = 121/7<BR>\n" );
document.write( "T3 = 7 + 2 * 72/7 = 193/7<BR>\n" );
document.write( "T4 = 7 + 3 * 72/7 = 265/7<BR>\n" );
document.write( "T5 = 7 + 4 * 72/7 = 337/7<BR>\n" );
document.write( "T6 = 7 + 5 * 72/7 = 409/7<BR>\n" );
document.write( "T7 = 7 + 6 * 72/7 = 481/7<BR>\n" );
document.write( "T8 = 7 + 7 * 72/7 = 553/7\r<BR>\n" );
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document.write( "add them up and you get a total of 2408/7 which is equal to 344.\r<BR>\n" );
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document.write( "the formulas look good.\r<BR>\n" );
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