document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041317>Question 1041317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the sum of the geometric series linked below?\r<BR>\n" );
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document.write( "A.) 198.4375<BR>\n" );
document.write( "B.) 96.875<BR>\n" );
document.write( "C.) 196.875<BR>\n" );
document.write( "D.) 396.875 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656283 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=656283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solution is 196.875<BR>\n" );
document.write( "you can use the sum of a geometric series formula, or you can just find A1 to A6 and add them up.\r<BR>\n" );
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document.write( "the formula for An is An = A1 * r^(n-1)<BR>\n" );
document.write( "A1 = 100<BR>\n" );
document.write( "r = 1/2\r<BR>\n" );
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document.write( "you get:<BR>\n" );
document.write( "A1 = 100 * (1/2)^0 = 100 * 1 = 100<BR>\n" );
document.write( "A2 = 100 * (1/2)^1 = 50 * 1/2 = 50<BR>\n" );
document.write( "A3 = 100 * (1/2)^2 = 100 * 1/4 = 25<BR>\n" );
document.write( "A4 = 100 * (1/2)^3 = 100 * 1/8 = 12.5<BR>\n" );
document.write( "A5 = 100 * (1/2)^4 = 100 * 1/16 = 6.25<BR>\n" );
document.write( "A6 = 100 * (1/2)^5 = 100 * 1/32 = 3.125\r<BR>\n" );
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document.write( "add them up and you get 196.875\r<BR>\n" );
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document.write( "the sum of a geometric series formula is Sn = (A1 * (1 - r^n)) / (1-r)<BR>\n" );
document.write( "A1 = 100<BR>\n" );
document.write( "r = 1/2<BR>\n" );
document.write( "n = 6\r<BR>\n" );
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document.write( "formula becomes S6 = (100 * (1 - (1/2)^6) / (1-r)<BR>\n" );
document.write( "simplify to get S6 = (100 * (1 - 1/64) / (1 - 1/2)<BR>\n" );
document.write( "simplify further to get S6 = (100 * 63/64) / (1/2)<BR>\n" );
document.write( "simplify further to get S6 = 100 * 63/64 * 2<BR>\n" );
document.write( "simplify further to get S6 = 100 * 126/64<BR>\n" );
document.write( "simplify further to get S6 = 196.875\r<BR>\n" );
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document.write( "you got the same answer two different ways.<BR>\n" );
document.write( "it looks good.\r<BR>\n" );
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