document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154055>Question 1154055</A>: <I><SPAN STYLE=\"word-break: break-all;\">  -39, -44, -49, -54, ...\r<BR>\n" );
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document.write( " Find  a35   <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776414 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=776414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are 2 ways to do this kind of problem. \r<BR>\n" );
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document.write( "The first method involves listing out 35 terms, each new term is found by subtracting 5 from the previous term (eg: -39 - 5 = -44, or -44-5 = -49, and so on). This is not recommended because there are so many terms. It's easy to lose track. \r<BR>\n" );
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document.write( "A much better method is to use the general nth term formula of an arithmetic sequence. That formula is<BR>\n" );
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document.write( "The first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+-39 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+-39\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The common difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+-5 ALIGN=MIDDLE  ALT=\"d+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we add on -5 each time, or subtract 5 each time, to get the next term. \r<BR>\n" );
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document.write( "So,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-39+%2B+%28-5%29%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-39+%2B+%28-5%29%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-39-5n%2B5 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-39-5n%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-5n-34 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-5n-34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------------------------------\r<BR>\n" );
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document.write( "As a check, let's plug in a random positive integer between 1 and 4 to see if it matches up with the proper element in the sequence we're given. I'll do n = 3 <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+-5%283%29-34 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+-5%283%29-34\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace n with 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+-15-34 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+-15-34\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D+=+-49 ALIGN=MIDDLE  ALT=\"a%5B3%5D+=+-49\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The third term is <font color=blue>-49</font>\r<BR>\n" );
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document.write( "Sure enough, the third term of the given sequence {-39, -44, <font color=blue>-49</font>, -54, ...} is <font color=blue>-49</font>. I'll let you check the other values of n (1, 2 and 4) to see if things line up properly or not.\r<BR>\n" );
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document.write( "Once we know the nth term formula, we plug in n = 35 to get the 35th term of the arithmetic sequence<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-5n-34 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-5n-34\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B35%5D+=+-5%2835%29-34 ALIGN=MIDDLE  ALT=\"a%5B35%5D+=+-5%2835%29-34\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace n with 35\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B35%5D+=+-175-34 ALIGN=MIDDLE  ALT=\"a%5B35%5D+=+-175-34\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B35%5D+=+-209 ALIGN=MIDDLE  ALT=\"a%5B35%5D+=+-209\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The 35th term is <font size=4 color=red>-209</font><BR>\n" );
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