document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=951201>Question 951201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> WRITING RULES: Write the next term in the sequence. Then write a rule for the nth term.<BR>\n" );
document.write( "-5, 10, -15, 20, . . . <BR>\n" );
document.write( "(I understand that the sequence is multiples of 5, but I don't understand how they got the negative for every other number) THANKS!! :D :3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580856 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=580856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The multiples of 5 can be represented by the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n ALIGN=MIDDLE  ALT=\"5n\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a whole number\r<BR>\n" );
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document.write( "Ex: if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+2 ALIGN=MIDDLE  ALT=\"n+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n+=+5%282%29+=+10 ALIGN=MIDDLE  ALT=\"5n+=+5%282%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How do we alternate the signs? We introduce the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En ALIGN=MIDDLE  ALT=\"%28-1%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If n is even, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En=1 ALIGN=MIDDLE  ALT=\"%28-1%29%5En=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie positive 1). If n is odd, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En=-1 ALIGN=MIDDLE  ALT=\"%28-1%29%5En=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. There are no other outcomes for this piece. So this is why <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En ALIGN=MIDDLE  ALT=\"%28-1%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perfect thing to tack on to help alternate the signs.\r<BR>\n" );
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document.write( "The nth term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En%2A%285n%29 ALIGN=MIDDLE  ALT=\"%28-1%29%5En%2A%285n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how I am multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En ALIGN=MIDDLE  ALT=\"%28-1%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n ALIGN=MIDDLE  ALT=\"5n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To confirm this, let's plug in n = 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En%2A%285n%29+=+%28-1%29%5E2%2A%285%2A2%29+=+1%2A10+=+10 ALIGN=MIDDLE  ALT=\"%28-1%29%5En%2A%285n%29+=+%28-1%29%5E2%2A%285%2A2%29+=+1%2A10+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now let's plug in n = 3 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En%2A%285n%29+=+%28-1%29%5E3%2A%285%2A3%29+=+-1%2A15+=+-15 ALIGN=MIDDLE  ALT=\"%28-1%29%5En%2A%285n%29+=+%28-1%29%5E3%2A%285%2A3%29+=+-1%2A15+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "I'll let you check the others.\r<BR>\n" );
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document.write( "The next term is -25 as I'm sure you've already figured that out. Let's use n = 5 to confirm\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5En%2A%285n%29+=+%28-1%29%5E5%2A%285%2A5%29+=+-1%2A25+=+-25 ALIGN=MIDDLE  ALT=\"%28-1%29%5En%2A%285n%29+=+%28-1%29%5E5%2A%285%2A5%29+=+-1%2A25+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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