document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102476>Question 1102476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The 5th term in a sequence is 25, and each term is 3 less than the previous term. Write an explicit rule and a recursive rule to describe the sequence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717173 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=717173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WITHOUT MEMORIZED FORMULAS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5Bn-1%5D-3 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5Bn-1%5D-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%2B1%5D=a%5Bn%5D-3%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%2B1%5D=a%5Bn%5D-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would be the recursive rule spelled out in<BR>\n" );
document.write( "\"each term is 3 less than the previous term.\"<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-5 ALIGN=MIDDLE  ALT=\"n-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms after the 5th term, we would have<BR>\n" );
document.write( "subtracted from 25 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-5 ALIGN=MIDDLE  ALT=\"n-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > times 3, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=25-3%28n-5%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=25-3%28n-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=25-3n-5 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=25-3n-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to the simplest explicit rule<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=20-3n ALIGN=MIDDLE  ALT=\"a%5Bn%5D=20-3n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Your teacher may have in mind a lot of formula memorizing and writing, like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-3 ALIGN=MIDDLE  ALT=\"d=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common difference.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the memorizable recursive rule formula for any arithmetic sequence,<BR>\n" );
document.write( "so in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2B%28-3%29 ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2B%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%2B1%5D=a%5Bn%5D-3%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%2B1%5D=a%5Bn%5D-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For all arithmetic sequences,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the memorizable explicit rule for any arithmetic sequence.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=25 ALIGN=MIDDLE  ALT=\"a%5B5%5D=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-3 ALIGN=MIDDLE  ALT=\"d=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D%2B%285-1%29%28-3%29 ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D%2B%285-1%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=a%5B1%5D%2B4%28-3%29 ALIGN=MIDDLE  ALT=\"25=a%5B1%5D%2B4%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=a%5B1%5D-12 ALIGN=MIDDLE  ALT=\"25=a%5B1%5D-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2B12=a%5B1%5D ALIGN=MIDDLE  ALT=\"25%2B12=a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=37 ALIGN=MIDDLE  ALT=\"a%5B1%5D=37\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Plugging <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=37+and+%7B%7B%7Bd=-3 ALIGN=MIDDLE  ALT=\"a%5B1%5D=37+and+%7B%7B%7Bd=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "into the memorized <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get explicit rule<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%5D=37-3%28n-1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%5D=37-3%28n-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "not that simple, but maybe the expected answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );