document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798537>Question 798537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation for the nth term of the arithmetic sequence.  <BR>\n" );
document.write( "-11, -15, -19, -23\r<BR>\n" );
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document.write( "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 #482266 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=482266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-11 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term.<BR>\n" );
document.write( "You add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to that to get the second term.<BR>\n" );
document.write( "You add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each term to get the next term.<BR>\n" );
document.write( "The common difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-4 ALIGN=MIDDLE  ALT=\"d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The recurrent formula for the sequence is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D-4 ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which just says that to get the next term you add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the term before.<BR>\n" );
document.write( " <BR>\n" );
document.write( "To get to the nth term, starting with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-11 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "you would have added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-4 ALIGN=MIDDLE  ALT=\"d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1 ALIGN=MIDDLE  ALT=\"n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > times,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=-11-4%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-11-4%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an equation/formula to calculate the nth term.<BR>\n" );
document.write( "You can simplify it a bit:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=-11-4%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-11-4%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=a%5Bn%5D=-11-4n-4 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=-11-4n-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5Bn%5D=-15-4n%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5Bn%5D=-15-4n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE that I keep talking about \"add\" and never said \"subtract\".<BR>\n" );
document.write( "If you believe in negative numbers, you do not need to believe in the existence of an extra operation called \"subtraction\".<BR>\n" );
document.write( "Life gets easier if you write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11-4=-15 ALIGN=MIDDLE  ALT=\"-11-4=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > for short,<BR>\n" );
document.write( "but think of it as adding the numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11 ALIGN=MIDDLE  ALT=\"-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I'm telling this, you because I think by now you are old enough to know.<BR>\n" );
document.write( "Just humor your teacher as needed, but there is no such thing as subtraction. You are not subtracting a number; you are just adding the opposite number.<BR>\n" );
document.write( "You do not need to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2B%28-4%29=-15 ALIGN=MIDDLE  ALT=\"-11%2B%28-4%29=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, just know that subtraction is something they made you believe in when you were little.<BR>\n" );
document.write( "While we are at it, there is no division either. You do not divide by a number, you just multiply times its reciprocal. </SPAN>\n" );
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