document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=701614>Question 701614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a(subscript 1) = 28,  a(subscript k=1) = a(subscript k) - 4\r<BR>\n" );
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document.write( "Please tell me what these numbers indicate and help me solve this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432530 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=432530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You may have seen <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=28 ALIGN=MIDDLE  ALT=\"a%5B1%5D=28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%2B1%5D=a%5Bk%5D-4 ALIGN=MIDDLE  ALT=\"a%5Bk%2B1%5D=a%5Bk%5D-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A sequence of numbers increasing (or decreasing) from one to the next<BR>\n" );
document.write( "by the same difference is called an \"arithmetic sequence\"<BR>\n" );
document.write( "or an \"arithmetic progression\".<BR>\n" );
document.write( "Each number in the sequence is called a \"term\".<BR>\n" );
document.write( "It is considered that each term in an arithmetic sequence,<BR>\n" );
document.write( "is equal to the previous term PLUS a \"common difference,\"<BR>\n" );
document.write( "usually represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So if each term was 4 less than the previous one,<BR>\n" );
document.write( "the common difference would be <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( "Usually, the first term is represented by <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( "the second term is represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "the term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%5D ALIGN=MIDDLE  ALT=\"a%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B1%29 ALIGN=MIDDLE  ALT=\"%28k%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B%28k%2B1%29%5D ALIGN=MIDDLE  ALT=\"a%5B%28k%2B1%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "To define a never ending sequence, with infinite terms,<BR>\n" );
document.write( "a formula is given.<BR>\n" );
document.write( "The formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=2n-1 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=2n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you the sequence of the odd integers:<BR>\n" );
document.write( "1, 3, 5, 7, .....<BR>\n" );
document.write( "Otherwise you could be given the value of one term,<BR>\n" );
document.write( "and the formula to calculate each term from the one before,<BR>\n" );
document.write( "such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%2B1%5D=a%5Bk%5D-4 ALIGN=MIDDLE  ALT=\"a%5Bk%2B1%5D=a%5Bk%5D-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that says that to get the next term, you subtract <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( "So, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=28 ALIGN=MIDDLE  ALT=\"a%5B1%5D=28\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=28-4=24 ALIGN=MIDDLE  ALT=\"a%5B2%5D=28-4=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=24-4=20 ALIGN=MIDDLE  ALT=\"a%5B3%5D=24-4=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=20-4=16 ALIGN=MIDDLE  ALT=\"a%5B4%5D=20-4=16\"   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=16-4=12 ALIGN=MIDDLE  ALT=\"a%5B5%5D=16-4=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and so on.<BR>\n" );
document.write( "By the time you get to term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "you have subtracted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-1%29 ALIGN=MIDDLE  ALT=\"%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=28-4%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=28-4%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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