document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193885>Question 193885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the second term of the infinite geometric series, \r<BR>\n" );
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document.write( "a + ar + ar^2 + ar^3......\r<BR>\n" );
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document.write( "is eaqual to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145564 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the second term of the infinite geometric series, <BR>\n" );
document.write( "a + ar + ar^2 + ar^3...... <BR>\n" );
document.write( "is equal to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a?<BR>\n" );
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document.write( "2nd term: a(2) = ar = 4<BR>\n" );
document.write( "Sum : a/(1-r) = 18<BR>\n" );
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document.write( " Rearrange:<BR>\n" );
document.write( "a = 4/r<BR>\n" );
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document.write( "Substitute:<BR>\n" );
document.write( "(4/r)/(1-r) = 18<BR>\n" );
document.write( "4/r = 18 - 18r<BR>\n" );
document.write( "4 = 18r-18r^2<BR>\n" );
document.write( "18r^2 - 18r +4 = 0<BR>\n" );
document.write( "9r^2 - 9r + 2 = 0<BR>\n" );
document.write( "9r^2 - 6r - 3r + 2 = 0<BR>\n" );
document.write( "3r(3r-2)-(3r-2) = 0<BR>\n" );
document.write( "(3r-2)(3r-1) = 0<BR>\n" );
document.write( "r = 2/3 or r = 1/3<BR>\n" );
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document.write( "Since a = 4/r<BR>\n" );
document.write( "a = 6  when r = 2/3  or a = 12 when r = 1/3<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H </SPAN>\n" );
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