document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891573>Question 891573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this question?  Many of the terms have a # or a letter with a # or letter written just below it.  I will use \"sub\" showing what is written that is lowered.  It's like the opposite location from an exponent.   \r<BR>\n" );
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document.write( "List the first six terms of the sequence defined recursively by (1) z(sub 1)=0, z(sub 2)=1, z (sub 3)=2, and (2) for m>=4, z(sub m)=z (sub m-1) + 2z(sub m-2) + 3z (sub m-3).\r<BR>\n" );
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document.write( "I sure hope that doesn't sound confusing.  Any help you can give would be much appreciated.  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 #539883 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given the first 3 terms as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28z%5B1%5D=0%2Cz%5B2%5D=1%2Cz%5B3%5D=2%29 ALIGN=MIDDLE  ALT=\"system%28z%5B1%5D=0%2Cz%5B2%5D=1%2Cz%5B3%5D=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for the other terms you are given a recursive formula to calculate a term from the 3 previous terms:<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3E=4 ALIGN=MIDDLE  ALT=\"m%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5Bm%5D=z%5B%28m-1%29%5D+%2B+2z%5B%28m-2%29%5D%2B+3z%5B%28m-3%29%5D ALIGN=MIDDLE  ALT=\"z%5Bm%5D=z%5B%28m-1%29%5D+%2B+2z%5B%28m-2%29%5D%2B+3z%5B%28m-3%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Using that formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B4%5D=z%5B%284-1%29%5D%2B2z%5B%284-2%29%5D%2B3z%5B%284-3%29%5D=z%5B3%5D%2B2z%5B2%5D%2B+3z%5B1%5D=2%2B2%2A1%2B3%2A0=2%2B2=highlight%284%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B5%5D=z%5B%285-1%29%5D%2B2z%5B%285-2%29%5D%2B3z%5B%285-3%29%5D+=z%5B4%5D%2B2z%5B3%5D%2B3z%5B2%5D=4%2B2%2A2%2B3%2A1=4%2B4%2B3=highlight%2811%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B6%5D=z%5B%286-1%29%5D%2B2z%5B%286-2%29%5D%2B3z%5B%286-3%29%5D%0D%0A=z%5B5%5D%2B2z%5B4%5D%2B3z%5B3%5D=11%2B2%2A4%2B3%2A2=11%2B8%2B6=highlight%2825%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the first 6 terms are: 0, 1, 2, 4, 11, 25 . </SPAN>\n" );
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