document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108567>Question 1108567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the fifth term of a geometric sequence whose first term is 32,768 and common ratio is one fourth? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723546 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=723546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the first term is 32768 and the common ratio is 1/4, then each succeeding term in the sequence is 1/4 * the value of the preceding term.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you let the first term be x, then the second term is 1/4 * x and the 3d term is 1/4 * that and the 4th term is 1/4 * that and the 5th term is 1/4 * that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get x * 1/4 * 1/4 * 1/4 * 1/4 which is equal to x * (1/4) ^ 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so the first term in the geometric sequence is 32768 * (1/4) ^ 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes it equal top 128.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general formula says An = A1 * r ^ (n-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A1 = 32768<BR>\n" );
document.write( "r = 1/4<BR>\n" );
document.write( "n = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using this formula, you get A5 = 32768 * (1/4) ^ 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you work by multiplying each succeeding term by 1/4, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A1 = 32768<BR>\n" );
document.write( "A2 = A1 * 1/4 = 8192<BR>\n" );
document.write( "A3 = A2 * 1/4 = 2048<BR>\n" );
document.write( "A4 = A3 * 1/4 = 512<BR>\n" );
document.write( "A5 = A4 * 1/4 = 128\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );