document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020716>Question 1020716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636581 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=636581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n? <BR>\n" );
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document.write( "a(m) = a(1) + (m-1)d = n<BR>\n" );
document.write( "a(n) = a(1) + (n-1)d = m<BR>\n" );
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document.write( "Subtract to get:<BR>\n" );
document.write( "(m-1)d-(n-1)d = n-m<BR>\n" );
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document.write( "md-d-nd-d = n-m<BR>\n" );
document.write( "(m-n)d-2d = n-m <BR>\n" );
document.write( "----<BR>\n" );
document.write( "(m-n-2)d = n-m<BR>\n" );
document.write( "----<BR>\n" );
document.write( "d = (n-m)/(m-n-2)<BR>\n" );
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document.write( "Solve for \"a(1)\"::<BR>\n" );
document.write( "a(1) = m +(1-n)d<BR>\n" );
document.write( "a(1) = m + (1-n)[(n-m)/(m-n-2)]<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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