document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019525>Question 1019525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a certain ap the 32nd term is twice the 12th term prove that 70th term is twice the 31st term<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635483 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The usual formula for the nth term of an AP is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  For the purpose of proving the statement, we use the alternative formula \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5Bk%5D+%2B+%28n-k%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5Bk%5D+%2B+%28n-k%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where k = 1, 2, 3, ...., n-1.\r<BR>\n" );
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document.write( "We are also given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B32%5D+=+2a%5B12%5D ALIGN=MIDDLE  ALT=\"a%5B32%5D+=+2a%5B12%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using this formula,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B70%5D+=+a%5B32%5D%2B38d+=+2a%5B12%5D+%2B38d+=+2%28a%5B12%5D%2B19d%29+=+2a%5B31%5D ALIGN=MIDDLE  ALT=\"a%5B70%5D+=+a%5B32%5D%2B38d+=+2a%5B12%5D+%2B38d+=+2%28a%5B12%5D%2B19d%29+=+2a%5B31%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "and the statement is proved. </SPAN>\n" );
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