document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104282>Question 1104282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.<BR>\n" );
document.write( "an = 3a(n &#8722; 1) + 7  and  a1 = 4\r<BR>\n" );
document.write( "\n" );
document.write( "I thought it would be<BR>\n" );
document.write( "a1=4<BR>\n" );
document.write( "a2= 3(2-1)+7=10<BR>\n" );
document.write( "a3= 3(3-1)+7=13<BR>\n" );
document.write( "a4= 3(4-1)+7=16<BR>\n" );
document.write( "a5= 3(5-1)+7=19<BR>\n" );
document.write( "But those are wrong. What am I missing with this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719031 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=719031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "a(n) is the nth term while a(n-1) is the term just before the nth term. <BR>\n" );
document.write( "For example, if n = 5, then a(n) = a(5) is the fifth term while a(n-1) = a(5-1) = a(4) is the fourth term<BR>\n" );
document.write( "Think of a(n) as function notation like f(x). Saying a(n) does NOT mean multiply.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because this is a recursive sequence, we use each term to build the next term.<BR>\n" );
document.write( "If we wanted to know the 10th term, then we need to find the first term, then the second, then the third all the way up to the 9th. <BR>\n" );
document.write( "We cannot simply find the 10th term by plugging in n = 10. <BR>\n" );
document.write( "This is a lot of work which is why recursive sequences are often a pain. <BR>\n" );
document.write( "Luckily we have a small number of terms to work with.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=blue>a(1) = 4</font> is the given first term. We use this to find the second term<BR>\n" );
document.write( "a(n) = 3*a(n-1) + 7<BR>\n" );
document.write( "a(2) = 3*a(2-1) + 7 ... replace every n with 2<BR>\n" );
document.write( "a(2) = 3*a(1) + 7<BR>\n" );
document.write( "a(2) = 3*<font color=blue>a(1)</font> + 7 ... notice we have a(1)<BR>\n" );
document.write( "a(2) = 3*<font color=blue>4</font> + 7 ... replace a(1) with 4<BR>\n" );
document.write( "a(2) = 12+7<BR>\n" );
document.write( "a(2) = 19<BR>\n" );
document.write( "So the second term is 19\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We repeat the same idea for the third term. Use the second term to find the third<BR>\n" );
document.write( "a(n) = 3*a(n-1) + 7<BR>\n" );
document.write( "a(3) = 3*a(3-1) + 7 ... replace every n with 3<BR>\n" );
document.write( "a(3) = 3*a(2) + 7 ... notice we have a(2)<BR>\n" );
document.write( "a(3) = 3*19 + 7 ... replace that a(2) with 19<BR>\n" );
document.write( "a(3) = 57 + 7<BR>\n" );
document.write( "a(3) = 64<BR>\n" );
document.write( "The third term is 64\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And again for the fourth<BR>\n" );
document.write( "a(n) = 3*a(n-1) + 7<BR>\n" );
document.write( "a(4) = 3*a(4-1) + 7 ... replace every n with 4<BR>\n" );
document.write( "a(4) = 3*a(3) + 7<BR>\n" );
document.write( "a(4) = 3*64 + 7 ... replace a(3) with 64<BR>\n" );
document.write( "a(4) = 192 + 7<BR>\n" );
document.write( "a(4) = 199<BR>\n" );
document.write( "The fourth term is 199\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then finally the fifth<BR>\n" );
document.write( "a(n) = 3*a(n-1) + 7<BR>\n" );
document.write( "a(5) = 3*a(5-1) + 7 ... replace every n with 5<BR>\n" );
document.write( "a(5) = 3*a(4) + 7<BR>\n" );
document.write( "a(5) = 3*199 + 7 ... replace a(4) with 199<BR>\n" );
document.write( "a(5) = 597 + 7<BR>\n" );
document.write( "a(5) = 604<BR>\n" );
document.write( "The fifth term is 604\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the first five terms are: <font size=4 color=red>4, 19, 64, 199, and 604</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );