document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125984>Question 1125984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x+6,x and x-3 are the first three terms of geometric progression.calculate the volume of x?.(i)find the value of x. (ii)the fifth term .(iii) the sum of infinity\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742320 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The n-th term of a geometric progression is given by a_n = a*r^(n-1) <BR>\n" );
document.write( "where a = the first term, r = the common ratio<BR>\n" );
document.write( "The first 3 terms are x+6, x, and x+6<BR>\n" );
document.write( "The first term a = x+6<BR>\n" );
document.write( "The second term is a_2 = ar = x<BR>\n" );
document.write( "The third term is a_3 = ar^2 = x-3<BR>\n" );
document.write( "The common ratio, r = x/(x+6)<BR>\n" );
document.write( "We solve for x by eliminating a and r:<BR>\n" );
document.write( "(x+6)r = x -> r = x/(x+6)<BR>\n" );
document.write( "(x+6)(x/(x+6))^2 = x-3<BR>\n" );
document.write( "x^2/(x+6) = x-3<BR>\n" );
document.write( "x^2 = x^2 + 3x - 18<BR>\n" );
document.write( "This gives x = 6, and thus a = 12, and r = 1/2<BR>\n" );
document.write( "Thus the 5th term is a_5 = 12(1/2)^4 = 3/4<BR>\n" );
document.write( "The infinite sum is S = a/(1-r) = 12/(1/2) = 24 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );