document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084171>Question 1084171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please give the recursive formula in both subscript and function.<BR>\n" );
document.write( "2,-6,18,-54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698242 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=698242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "In subscript form, the recursive formula would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a_{1} = 2\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a_{n} = -3*\left(a_{n-1}\right)\"><BR>\n" );
document.write( "Which says \"The starting term is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a_1 = 2\">. To get the nth term <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a_n\">, we need to multiply the previous term <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a_{n-1}\"> by -3.\"<BR>\n" );
document.write( "In this case, n is some positive whole number (n > 0).\r<BR>\n" );
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document.write( "With function form, we have the same basic format just with different notation<BR>\n" );
document.write( "The function form would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+2 ALIGN=MIDDLE  ALT=\"f%281%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29+=+-3%2Af%28n-1%29 ALIGN=MIDDLE  ALT=\"f%28n%29+=+-3%2Af%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where n > 0 is a whole number.\r<BR>\n" );
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document.write( "If we plug in n = 2 to get the second term, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29+=+-3%2Af%28n-1%29 ALIGN=MIDDLE  ALT=\"f%28n%29+=+-3%2Af%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+-3%2Af%282-1%29 ALIGN=MIDDLE  ALT=\"f%282%29+=+-3%2Af%282-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > replace every n with 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+-3%2Af%281%29 ALIGN=MIDDLE  ALT=\"f%282%29+=+-3%2Af%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+-3%2A%282%29 ALIGN=MIDDLE  ALT=\"f%282%29+=+-3%2A%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(1) with 2 (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+2 ALIGN=MIDDLE  ALT=\"f%281%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is defined above)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+-6 ALIGN=MIDDLE  ALT=\"f%282%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we get the proper second term, which is -6\r<BR>\n" );
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document.write( "If we plug in n = 3 to get the third term, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29+=+-3%2Af%28n-1%29 ALIGN=MIDDLE  ALT=\"f%28n%29+=+-3%2Af%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+-3%2Af%283-1%29 ALIGN=MIDDLE  ALT=\"f%283%29+=+-3%2Af%283-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > replace every n with 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+-3%2Af%282%29 ALIGN=MIDDLE  ALT=\"f%283%29+=+-3%2Af%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+-3%2A%28-6%29 ALIGN=MIDDLE  ALT=\"f%283%29+=+-3%2A%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(2) with -6 (since we just found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+-6 ALIGN=MIDDLE  ALT=\"f%282%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > above)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+18 ALIGN=MIDDLE  ALT=\"f%283%29+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we get the proper third term, which is 18\r<BR>\n" );
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document.write( "The rest of the terms are generated in this recursive fashion.\r<BR>\n" );
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