document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209400>Question 1209400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let a_1, a_2, a_3, \dots be a sequence. If<BR>\n" );
document.write( "a_n = a_{n - 1} + a_{n - 2}<BR>\n" );
document.write( "for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848756 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I doubt if there is a faster way to solve the problem than what is shown by the other tutor... but his response has a lot of unnecessary discussion at the beginning.<br><BR>\n" );
document.write( "The given recursive formula tells us how to get the next numbers in the sequence from the previous numbers in the sequence:<br><BR>\n" );
document.write( "a_n = a_(n-1) + a_(n-2)<br><BR>\n" );
document.write( "Turn that recursive formula around so it tells you how to find PREVIOUS numbers in the sequence from known numbers in the sequence:<br><BR>\n" );
document.write( "a_(n-2) = a_n - a_(n-1)<br><BR>\n" );
document.write( "Then, starting with the given a_11 = 4 and a_10 = 1...<br><BR>\n" );
document.write( "a_9 = a_11 - a_10 = 4-1 = 3<br><BR>\n" );
document.write( "a_8 = a_10 - a_9 = 1-3 = -2<br><BR>\n" );
document.write( "a_7 = a_9 - a_8 = 3-(-2) = 5<br><BR>\n" );
document.write( "a_6 = a_8 - a_7 = -2-5 = -7<br><BR>\n" );
document.write( "ANSWER: a_6 = -7<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );