document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209845>Question 1209845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The second and seventh term of a geometric progression are 18 and 4374 respectively. Find the sum of the fourth and the eighth term when the difference is 3<BR>\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 #850819 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step-by-step.\r<BR>\n" );
document.write( "\n" );
document.write( "Understanding Geometric Progressions\r<BR>\n" );
document.write( "\n" );
document.write( "A geometric progression (GP) is a sequence where each term is found by multiplying the previous term by a constant called the common ratio (r). The general form of a GP is:\r<BR>\n" );
document.write( "\n" );
document.write( "a, ar, ar^2, ar^3, ...\r<BR>\n" );
document.write( "\n" );
document.write( "where:\r<BR>\n" );
document.write( "\n" );
document.write( "a is the first term<BR>\n" );
document.write( "r is the common ratio<BR>\n" );
document.write( "Given Information\r<BR>\n" );
document.write( "\n" );
document.write( "The second term (ar) is 18.<BR>\n" );
document.write( "The seventh term (ar^6) is 4374.<BR>\n" );
document.write( "Finding a and r\r<BR>\n" );
document.write( "\n" );
document.write( "Set up equations:\r<BR>\n" );
document.write( "\n" );
document.write( "ar = 18 (Equation 1)<BR>\n" );
document.write( "ar^6 = 4374 (Equation 2)<BR>\n" );
document.write( "Divide Equation 2 by Equation 1:\r<BR>\n" );
document.write( "\n" );
document.write( "(ar^6) / (ar) = 4374 / 18<BR>\n" );
document.write( "r^5 = 243<BR>\n" );
document.write( "Solve for r:\r<BR>\n" );
document.write( "\n" );
document.write( "r = ∛⁵243 = 3<BR>\n" );
document.write( "Substitute r back into Equation 1 to find a:\r<BR>\n" );
document.write( "\n" );
document.write( "a(3) = 18<BR>\n" );
document.write( "a = 18 / 3 = 6<BR>\n" );
document.write( "Finding the Fourth and Eighth Terms\r<BR>\n" );
document.write( "\n" );
document.write( "Fourth term (ar^3):\r<BR>\n" );
document.write( "\n" );
document.write( "ar^3 = 6 * 3^3 = 6 * 27 = 162<BR>\n" );
document.write( "Eighth term (ar^7):\r<BR>\n" );
document.write( "\n" );
document.write( "ar^7 = 6 * 3^7 = 6 * 2187 = 13122<BR>\n" );
document.write( "Finding the Sum\r<BR>\n" );
document.write( "\n" );
document.write( "We are asked to find the sum of the fourth and eighth terms when the difference is 3. We have already determined that r=3, so we can use the values calculated above.\r<BR>\n" );
document.write( "\n" );
document.write( "Sum = 162 + 13122 = 13284<BR>\n" );
document.write( "Answer\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of the fourth and eighth term is 13284. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );