document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41804>Question 41804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a(1) in a geometric series for which S(n) = 189, r = 1/2, and a(n) =3.\r<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 #27078 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find a(1) in a geometric series for which S(n) =189, r=1/2, and a(n)=3.<BR>\n" );
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document.write( "AN=A1*R^(N-1)<BR>\n" );
document.write( "3=A1*(1/2)^(N-1)=A1*0.5^(N-1)..............................I<BR>\n" );
document.write( "SN=A1*{1-R^N}/(1-R)<BR>\n" );
document.write( "189=A1*{1-(1/2)^N }/(1-0.5)=2A1*(1-0.5^N).........................II<BR>\n" );
document.write( "EQN.II/EQN.I<BR>\n" );
document.write( "189/3=2A1(1-0.5^N)/{A1*0.5^(N-1)}=63<BR>\n" );
document.write( "2(1-(0.5^(N-1))*(0.5))=63*0.5^(N-1)<BR>\n" );
document.write( "LET 0.5^(N-1)=X<BR>\n" );
document.write( "2(1-0.5X)=63X<BR>\n" );
document.write( "2-X=63X<BR>\n" );
document.write( "64X=2<BR>\n" );
document.write( "X=2/64=1/32=0.5^(N-1)<BR>\n" );
document.write( "0.5^(N-1)=(1/2)^5=0.5^5<BR>\n" );
document.write( "N-1=5<BR>\n" );
document.write( "N=6<BR>\n" );
document.write( "PUTTING IN EQN.I<BR>\n" );
document.write( "3=A1*(0.5)^5=A1/32<BR>\n" );
document.write( "A1=32*3=96  </SPAN>\n" );
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