document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256103>Question 256103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, My sister has an exam tomorrow and I am helping her study.We are having a problem with sequence equations. It gives a sequence like 2,5,8,11 and wants us to find the 23rd term. now I understand the first part which is to figure out the the number between the two terms and times it with the term you want to find, but then for some reason her book says to add a number to get the answer and I am so confused. the most I can get is t=3n and then I am stuck please help us.<BR>\n" );
document.write( "                                           thank you<BR>\n" );
document.write( "                                                Kaitlynn  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188265 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=188265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets assume the sequence 2,5,8,11,... is an arithmetic sequence. The general form of the arithmetic sequence is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=d%2An%2Ba%5B1%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D=d%2An%2Ba%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the nth term, d is the difference, and <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;\" > is the first term\r<BR>\n" );
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document.write( "So lets find the difference between 2 terms (i.e. the difference between two terms)\r<BR>\n" );
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document.write( "To find the difference, simply pick any term and subtract the previous term from that selected term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2=3 ALIGN=MIDDLE  ALT=\"5-2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Select the 2nd term (which is 5) and subtract the 1st term (which is 2) from it.\r<BR>\n" );
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document.write( "So we get a difference of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets pick another pair of terms to verify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-5=3 ALIGN=MIDDLE  ALT=\"8-5=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Select the 3rd term (which is 8) and subtract the 2nd term (which is 5) from it.\r<BR>\n" );
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document.write( "And again, we get a difference of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets pick another pair of terms to verify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11-8=3 ALIGN=MIDDLE  ALT=\"11-8=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Select the 4th term (which is 11) and subtract the 3rd term (which is 8) from it.\r<BR>\n" );
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document.write( "And again, we get a difference of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we've tested every consecutive pair of terms, we've verified that the sequence has a constant difference of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means the sequence is arithmetic\r<BR>\n" );
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document.write( "Since the difference is <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;\" > and the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means the arithmetic sequence is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3n%2B2 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3n%2B2\"   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;\" > starts at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the list of numbers 2,5,8,11... can be generated by the sequence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3n%2B2 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3n%2B2\"   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;\" > starts at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since n=0 generates the first term, this means that the 23rd term is generated when n=22\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3n%2B2 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3n%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B22%5D=3%2822%29%2B2 ALIGN=MIDDLE  ALT=\"a%5B22%5D=3%2822%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=22 ALIGN=MIDDLE  ALT=\"n=22\"   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%5B22%5D=66%2B2 ALIGN=MIDDLE  ALT=\"a%5B22%5D=66%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B22%5D=68 ALIGN=MIDDLE  ALT=\"a%5B22%5D=68\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the 23rd term is 68 </SPAN>\n" );
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