document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206538>Question 1206538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geometric Sequence in which T5 = 8T2<BR>\n" );
document.write( "T4 + T6 = 240\r<BR>\n" );
document.write( "\n" );
document.write( "Find the Sequence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844083 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=844083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "T1 = first term<BR>\n" );
document.write( "T2 = second term<BR>\n" );
document.write( "T3 = third term<BR>\n" );
document.write( "etc\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To go from term to term in a geometric sequence, we multiply by a common ratio r.<BR>\n" );
document.write( "T2 = r*T1<BR>\n" );
document.write( "T3 = r*T2 = r*(r*T1) = r^2*T1<BR>\n" );
document.write( "T4 = r*T3 = r*(r^2*T1) = r^3*T1<BR>\n" );
document.write( "T5 = r*T4 = r*(r^3*T1) = r^4*T1<BR>\n" );
document.write( "etc\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To avoid a sequence of nothing but 0s, we require that r and T1 are both nonzero. <BR>\n" );
document.write( "By extension it will mean r*T1 is also nonzero.<BR>\n" );
document.write( "This will allow us to divide both sides by r*T1 as shown in the next section.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "T5 = 8*T2<BR>\n" );
document.write( "r^4*T1 = 8*r*T1<BR>\n" );
document.write( "r^3 = 8 .................... divide both sides by r*T1<BR>\n" );
document.write( "r = cubeRoot(8)<BR>\n" );
document.write( "r = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the second given equation.<BR>\n" );
document.write( "T4 + T6 = 240<BR>\n" );
document.write( "r^3*T1 + r^5*T1 = 240<BR>\n" );
document.write( "2^3*T1 + 2^5*T1 = 240<BR>\n" );
document.write( "8*T1 + 32*T1 = 240<BR>\n" );
document.write( "40*T1 = 240<BR>\n" );
document.write( "T1 = 240/40<BR>\n" );
document.write( "T1 = 6 is the first term of the geometric sequence.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The geometric sequence is therefore:<BR>\n" );
document.write( "<font color=red>6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, ...</font><BR>\n" );
document.write( "Start at 6. Double each term to get the next term.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Verification:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Focus on the terms T2 and T5 highlighted in <font color=blue>blue</font><BR>\n" );
document.write( "6, <font color=blue>12</font>, 24, 48, <font color=blue>96</font>, 192, 384, 768, 1536, 3072, ...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then notice:<BR>\n" );
document.write( "T5 = 8*T2<BR>\n" );
document.write( "96 = 8*12<BR>\n" );
document.write( "96 = 96<BR>\n" );
document.write( "The first requirement is verified.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's highlight the 4th and 6th terms.<BR>\n" );
document.write( "6, 12, 24, <font color=blue>48</font>, 96, <font color=blue>192</font>, 384, 768, 1536, 3072, ...<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "T4 + T6 = 240<BR>\n" );
document.write( "48 + 192 = 240<BR>\n" );
document.write( "240 = 240<BR>\n" );
document.write( "The second requirement is verified.<BR>\n" );
document.write( "The answer is fully confirmed.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );