document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976324>Question 976324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the series {ak} satisfies a1=1, a2=2, and (ak)-4(ak-1)+3(ak-2)=0 for K greater than or equal to 3, then ak=(1+p)/q for k greater than or equal to 1. Find p and q.<BR>\n" );
document.write( "Please use the below representation-<BR>\n" );
document.write( "ak = kth term = a subscript k<BR>\n" );
document.write( "a1 = 1st term = a subscript 1<BR>\n" );
document.write( "a2 = 2nd term = a subscript 2<BR>\n" );
document.write( "ak-1 = (k-1)th term = a subscript k-1<BR>\n" );
document.write( "ak-2 = (k-2)th term = a subscript k-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597930 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=597930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the series {ak} satisfies a1=1, a2=2, and (ak)-4(ak-1)+3(ak-2)=0 for K greater than or equal to 3, then ak=(1+p)/q for k greater than or equal to 1. Find p and q.<BR>\n" );
document.write( "Please use the below representation-<BR>\n" );
document.write( "ak = kth term = a subscript k<BR>\n" );
document.write( "a1 = 1st term = a subscript 1<BR>\n" );
document.write( "a2 = 2nd term = a subscript 2<BR>\n" );
document.write( "ak-1 = (k-1)th term = a subscript k-1<BR>\n" );
document.write( "ak-2 = (k-2)th term = a subscript k-2 <BR>\n" );
document.write( "------<BR>\n" );
document.write( "a(3) - 4*a(2) + 3*a(1) = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a(3) - 4*2 + 3*1 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a(3) - 8 + 3 = 0<BR>\n" );
document.write( "a(3) = 5<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "ak=(1+p)/q <BR>\n" );
document.write( "Therefore::<BR>\n" );
document.write( "a(3) = (1+p)/q = 5/1<BR>\n" );
document.write( "------<BR>\n" );
document.write( "1+p = 5, so p = 4<BR>\n" );
document.write( "q = 1<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );