document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983883>Question 983883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The nth term of an arithmetical progression is n and the nth term is m. Find the first term and the common difference. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604898 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=604898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> TYPO!<BR>\n" );
document.write( "\"The<BR>\n" );
document.write( "nth term of an arithmetical progression is n     and the<BR>\n" );
document.write( "nth term is m.\"\r<BR>\n" );
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document.write( "So, the nth term is n = m ,<BR>\n" );
document.write( "and we do not have enough information about the rest of the arithmetic progression?<BR>\n" );
document.write( "I guess the problem should read differently,<BR>\n" );
document.write( "and I believe I am a good guesser,<BR>\n" );
document.write( "but from so little information, all I can manage is some wild guesses.\r<BR>\n" );
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document.write( "GUESS # 1:<BR>\n" );
document.write( "Maybe it should read <BR>\n" );
document.write( "\"The nth term of an arithmetical progression is n,<BR>\n" );
document.write( "and the kth term is m.\"<BR>\n" );
document.write( "Maybe with a number instead of k, or maybe k is m.<BR>\n" );
document.write( "Then, with <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;\" > being the first term,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > being the common difference,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2Bd%2A%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2Bd%2A%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the nth term, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=a%5B1%5D%2Bd%2A%28n-1%29 ALIGN=MIDDLE  ALT=\"n=a%5B1%5D%2Bd%2A%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%5D=a%5B1%5D%2Bd%2A%28k-1%29 ALIGN=MIDDLE  ALT=\"a%5Bk%5D=a%5B1%5D%2Bd%2A%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the kth term, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=a%5B1%5D%2Bd%2A%28k-1%29 ALIGN=MIDDLE  ALT=\"m=a%5B1%5D%2Bd%2A%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-m=%28a%5B1%5D%2Bd%2A%28n-1%29%29-%28a%5B1%5D%2Bd%2A%28k-1%29%29 ALIGN=MIDDLE  ALT=\"n-m=%28a%5B1%5D%2Bd%2A%28n-1%29%29-%28a%5B1%5D%2Bd%2A%28k-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-m=a%5B1%5D%2Bd%2A%28n-1%29-a%5B1%5D-d%2A%28k-1%29 ALIGN=MIDDLE  ALT=\"n-m=a%5B1%5D%2Bd%2A%28n-1%29-a%5B1%5D-d%2A%28k-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=n-m=d%2A%28n-1%29-d%2A%28k-1%29 ALIGN=MIDDLE  ALT=\"n-m=d%2A%28n-1%29-d%2A%28k-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=n-m=d%2A%28n-1-%28k-1%29%29 ALIGN=MIDDLE  ALT=\"n-m=d%2A%28n-1-%28k-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-m=d%2A%28n-1-k%2B1%29 ALIGN=MIDDLE  ALT=\"n-m=d%2A%28n-1-k%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-m=d%2A%28n-k%29 ALIGN=MIDDLE  ALT=\"n-m=d%2A%28n-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=%28n-m%29%2F%28n-k%29%29 ALIGN=MIDDLE  ALT=\"highlight%28d=%28n-m%29%2F%28n-k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=System%28n=a%5B1%5D%2Bd%2A%28n-1%29%2Cd=%28n-m%29%2F%28n-k%29%29 ALIGN=MIDDLE  ALT=\"System%28n=a%5B1%5D%2Bd%2A%28n-1%29%2Cd=%28n-m%29%2F%28n-k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=a%5B1%5D%2B%28%28n-m%29%2F%28n-k%29%29%2A%28n-1%29 ALIGN=MIDDLE  ALT=\"n=a%5B1%5D%2B%28%28n-m%29%2F%28n-k%29%29%2A%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=a%5B1%5D%2B%28n-m%29%2A%28n-1%29%2F%28n-k%29 ALIGN=MIDDLE  ALT=\"n=a%5B1%5D%2B%28n-m%29%2A%28n-1%29%2F%28n-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=n-%28n-m%29%2A%28n-1%29%2F%28n-k%29%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=n-%28n-m%29%2A%28n-1%29%2F%28n-k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The resulting formula for <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 messy,<BR>\n" );
document.write( "but I do not see a way to make it look simple.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "GUESS # 2:<BR>\n" );
document.write( "Maybe it should read <BR>\n" );
document.write( "\"The sum of the first n terms of an arithmetical progression is n,<BR>\n" );
document.write( "and the nth term is m.\"<BR>\n" );
document.write( "Then, with <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;\" > being the first term,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > being the common difference,<BR>\n" );
document.write( "the nth term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D=d%2A%28n-1%29=m ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D=d%2A%28n-1%29=m\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "the sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28a%5B1%5D%2Ba%5Bn%5D%29%2F2=n%2A%28a%5B1%5D%2Bm%29%2F2=n ALIGN=MIDDLE  ALT=\"n%2A%28a%5B1%5D%2Ba%5Bn%5D%29%2F2=n%2A%28a%5B1%5D%2Bm%29%2F2=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28a%5B1%5D%2Bm%29%2F2=n ALIGN=MIDDLE  ALT=\"n%2A%28a%5B1%5D%2Bm%29%2F2=n\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2Bm%29%2F2=n%2Fn ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2Bm%29%2F2=n%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2Bm%29%2F2=1 ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2Bm%29%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Bm=2 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Bm=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%5B1%5D=2-m%29 ALIGN=MIDDLE  ALT=\"highlight%28a%5B1%5D=2-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%5B1%5D%2Bd%2A%28n-1%29=m%2Ca%5B1%5D=2-m%29 ALIGN=MIDDLE  ALT=\"system%28a%5B1%5D%2Bd%2A%28n-1%29=m%2Ca%5B1%5D=2-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-m%2Bd%2A%28n-1%29=m ALIGN=MIDDLE  ALT=\"2-m%2Bd%2A%28n-1%29=m\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2A%28n-1%29=2m-2 ALIGN=MIDDLE  ALT=\"d%2A%28n-1%29=2m-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=%282m-2%29%2F%28n-1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28d=%282m-2%29%2F%28n-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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