document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54684>Question 54684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the nth term in an arithmetic sequence is represented by tn. If tp=p squared and tq=q squared find 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 #36983 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the first term of the A.P. series be 'a' and the common difference be 'd'.<BR>\n" );
document.write( "Then, the p-th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tp+=+a+%2B+%28p-1%29d ALIGN=MIDDLE  ALT=\"tp+=+a+%2B+%28p-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > and q-th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tq+=+a+%2B+%28q-1%29d ALIGN=MIDDLE  ALT=\"tq+=+a+%2B+%28q-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tp=p%5E2 ALIGN=MIDDLE  ALT=\"tp=p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tq=q%5E2 ALIGN=MIDDLE  ALT=\"tq=q%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+=+a+%2B+%28p-1%29d ALIGN=MIDDLE  ALT=\"p%5E2+=+a+%2B+%28p-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > --------(1)<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2+=+a+%2B+%28q-1%29d ALIGN=MIDDLE  ALT=\"q%5E2+=+a+%2B+%28q-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > --------{2)\r<BR>\n" );
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document.write( "Subtracting (2) from (1),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-q%5E2=%28p-1%29d+-+%28q-1%29d ALIGN=MIDDLE  ALT=\"p%5E2-q%5E2=%28p-1%29d+-+%28q-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2Bq%29%28p-q%29=%28p-q%29d ALIGN=MIDDLE  ALT=\"%28p%2Bq%29%28p-q%29=%28p-q%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+p%2Bq ALIGN=MIDDLE  ALT=\"d+=+p%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" > [since p is not equal to q]\r<BR>\n" );
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document.write( "So the reqd. common difference is (p+q). </SPAN>\n" );
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