document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092222>Question 1092222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a15 = 20, a30 = -13 then what is r, S50 (Geometric Sequence) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706800 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=706800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for An of a geometric sequence is:\r<BR>\n" );
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document.write( "An = A1 * r ^ (n-1)\r<BR>\n" );
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document.write( "the formula for Sn of a geometric sequence is:\r<BR>\n" );
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document.write( "Sn = A1 * (1 - r ^ n) / (1 - r)\r<BR>\n" );
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document.write( "we first need to find A1 and r and then we can find Sn.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "A15 = 20<BR>\n" );
document.write( "A30 = -13\r<BR>\n" );
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document.write( "if you know that An = A1 * r ^ (n-1), and you replace A1 with Am, then it follows that the formula should then read:\r<BR>\n" );
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document.write( "An = Am * r ^ (n-m)\r<BR>\n" );
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document.write( "therefore, you get:\r<BR>\n" );
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document.write( "A30 = A15 * r ^ (30 - 15)\r<BR>\n" );
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document.write( "this becomes A30 = A15 * r ^ (15)\r<BR>\n" );
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document.write( "since A30 = -13 and A15 = 20, you get -13 = 20 * r ^ (15)\r<BR>\n" );
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document.write( "divide both sides of this equation by 20 to get -13 /20 = r ^ (15)\r<BR>\n" );
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document.write( "take the 15th root of both sides of this equation to get (-13 / 20) ^ (1/15) = r\r<BR>\n" );
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document.write( "solve for r to get r = -.9716896058\r<BR>\n" );
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document.write( "now that you know r, you can solve for A1.\r<BR>\n" );
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document.write( "the formula of An = A1 * r ^ (n-1) becomes A15 = A1 * r ^ 14 when n = 15.\r<BR>\n" );
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document.write( "since A15 = 20 and r = -.9716896058, this formula then becomes 20 = A1 * -.9716896058 ^ 14.\r<BR>\n" );
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document.write( "divide both sides of this equation by -.9716896058 ^ 14 and you get 20 /(-.9716896058 ^ 14) = A1.\r<BR>\n" );
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document.write( "solve for A1 to get A1 = 29.89814172\r<BR>\n" );
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document.write( "now that you know A1 and r, you can solve for S50.\r<BR>\n" );
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document.write( "the formula for Sn is Sn = A1 * (1 - r^n) / (1 - r)\r<BR>\n" );
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document.write( "when n = 50 and A1 = 29.89814172 and r = -.9716896058, that formula becomes S50 = 29.89814172 * (1 - (-.9716896058) ^ 50) / (1 - (-.9716896058).\r<BR>\n" );
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document.write( "solve for S50 to get S50 = 11.55640593\r<BR>\n" );
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document.write( "i took the trouble to do the actual n by n calculations for you in excel so you could see the progression.\r<BR>\n" );
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document.write( "this is what it looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/090201.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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