document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737267>Question 737267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey, I am confused with this word problem in which I have to use arithmetic/geometric sequences. \r<BR>\n" );
document.write( "\n" );
document.write( "How many ancestors from parents to great-great-great-great grandparents do you have?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450259 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=450259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 parents\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4 grandparents (2*2 = 4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8 great-grandparents (2*2*2 = 8 ... each generation going back doubles the previous count)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16 great-great-grandparents (2*2*2*2 = 16)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "32 great-great-great-grandparents (2*2*2*2*2 = 32)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "64 great-great-great-great-grandparents (2*2*2*2*2*2 = 64)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add up the individual counts:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2+4+8+16+32+64 = <font color=\"red\">126 ancestors</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Shortcut:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can take the shortcut and sum the geometric sequence 1*2^(n-1) from n = 1 to n = 6 (since you're going back 6 generations), then subtract off 1 since you're not counting yourself as an ancestor (of you). You would use the formula below and plug in a = 1, r = 2 and n = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = a*(1-r^(n+1))/(1-r)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = 1*(1-2^(6+1))/(1-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = 1*(1-2^7)/(1-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = 1*(1-128)/(1-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = 1*(-127)/(-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = 127\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So if you summed up 1, 2, 4, 8, 16, 32, 64, then you would get 127...BUT you are NOT including yourself in this ancestor list. So you subtract 1 to get 127 - 1 = 126\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So either way, there are <font color=\"red\">126 ancestors</font> total. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );