document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398922>Question 398922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find S8 for the geometric series 256 + 64 + 16 + 4 +… </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282575 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=282575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a geometric series with a common ratio of 1/4.\r<BR>\n" );
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document.write( "formula for sum of a geometric series is:\r<BR>\n" );
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document.write( "Sn = (a*(1-r^n)) / (1-r)\r<BR>\n" );
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document.write( "n = number of terms in the series.<BR>\n" );
document.write( "S = sum of the terms in the series.<BR>\n" );
document.write( "a = the first term in the series.<BR>\n" );
document.write( "r = the common ratio in the series.\r<BR>\n" );
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document.write( "In this problem:\r<BR>\n" );
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document.write( "n = 8<BR>\n" );
document.write( "a = 256<BR>\n" );
document.write( "r = (.25)\r<BR>\n" );
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document.write( "Substitute in the formula to get:\r<BR>\n" );
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document.write( "Sn = (a(1-r^n)) / (1-r) becomes:\r<BR>\n" );
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document.write( "S8 = (256 * (1 - .25^8)) / (1 - .25)\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "S8 = (256 * (1 - .000015259) / (.75)\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( "S8 = (256 * .999984741) / (.75)\r<BR>\n" );
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document.write( "Solve to get:\r<BR>\n" );
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document.write( "S8 = 341.328125\r<BR>\n" );
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document.write( "You can verify this is correct by detailing each individual term from 1 to 8 and then summing them up.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "S1 = 256<BR>\n" );
document.write( "S2 = 64<BR>\n" );
document.write( "S3 = 16<BR>\n" );
document.write( "S4 = 4<BR>\n" );
document.write( "S5 = 1<BR>\n" );
document.write( "S6 = .25<BR>\n" );
document.write( "S7 = .0625<BR>\n" );
document.write( "S8 = .015625\r<BR>\n" );
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document.write( "Sum is equal to 341.328125\r<BR>\n" );
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document.write( "Answer is the same.\r<BR>\n" );
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document.write( "You're good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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