document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475149>Question 475149</A>: <I><SPAN STYLE=\"word-break: break-all;\">    What is Sn of the geometric series with a1 = –81, r = –2/3, and n = 5?\r<BR>\n" );
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document.write( "THANKS FOR THE HELP :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325803 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=325803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sn of a geometric series is given by the equation:<BR>\n" );
document.write( "Sn = a * (1-r^n) / (1-r)<BR>\n" );
document.write( "a if the first term in the sequence.<BR>\n" );
document.write( "r is the common ratio<BR>\n" );
document.write( "To see how this work, assume your sequence is:<BR>\n" );
document.write( "2,4,8,16<BR>\n" );
document.write( "The sum of this series is 30.<BR>\n" );
document.write( "Using the formula, we have:<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "n = 4<BR>\n" );
document.write( "r = 2<BR>\n" );
document.write( "Sn = a * (1-r^n) / (1-r) which becomes:<BR>\n" );
document.write( "Sn = 2 * (1-2^4) / (1-2) which becomes:<BR>\n" );
document.write( "Sn = 2 * (1-16)/(1-2) which becomes:<BR>\n" );
document.write( "Sn = 2 * (-15 / -1) which becomes:<BR>\n" );
document.write( "Sn = -30 / -1 which becomes:<BR>\n" );
document.write( "Sn = 30.<BR>\n" );
document.write( "The formula works and can be applied to your problem.<BR>\n" );
document.write( "Your problem states:<BR>\n" );
document.write( "a = –81<BR>\n" );
document.write( "r = –2/3<BR>\n" );
document.write( "n = 5 <BR>\n" );
document.write( "The formula is:<BR>\n" );
document.write( "Sn = a * (1-r^n) / (1-r)<BR>\n" );
document.write( "Substituting with your values in the equation gets:<BR>\n" );
document.write( "Sn = -81 * (1-(-2/3)^5) / (1-(-2/3))<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "Sn = (-81 * (1 - (-32/243))) / (1 + (2/3)) which becomes:<BR>\n" );
document.write( "Sn = (-81 * (1 + (32/243))) / (1 + (2/3)) which becomes:<BR>\n" );
document.write( "Sn = (-81 * (275/243)) / (5/3) which becomes:<BR>\n" );
document.write( "Sn = -81 * (275/243) * (3/5).<BR>\n" );
document.write( "275 can be divided by 5 and 243 can be divided by 3, so your equation becomes:<BR>\n" );
document.write( "Sn = -81 * (55/81) which then becomes:<BR>\n" );
document.write( "Sn = -55.<BR>\n" );
document.write( "The sum of the geometric series is equal to -55.<BR>\n" );
document.write( "We can check this out to see if it's true because the numbers are small enough.<BR>\n" );
document.write( "We start with -81 and then multiply it by the ratio of (-2/3) for 4 times.<BR>\n" );
document.write( "We get:<BR>\n" );
document.write( "-81<BR>\n" );
document.write( "54<BR>\n" );
document.write( "-36<BR>\n" );
document.write( "24<BR>\n" );
document.write( "-16<BR>\n" );
document.write( "The sum of these 5 terms is equal to -55.<BR>\n" );
document.write( "The formula works and you have your solution.<BR>\n" );
document.write( " </SPAN>\n" );
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