document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090199>Question 1090199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a,b,c are in A.P., show that\r<BR>\n" );
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document.write( "(i) 2(a-b) = a-c = 2(b-c)\r<BR>\n" );
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document.write( "(ii)(a-c)^2 = 4(b^2-ac) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704661 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is not stated whether the terms are consecutive, but we will proceed under that assumption.<BR>\n" );
document.write( "A general expression for the term a is a = a1 + (n-1)d, assuming a is the n-th term, and d is the common difference<BR>\n" );
document.write( "So b = a + d = and c = a + 2d<BR>\n" );
document.write( "(i) <BR>\n" );
document.write( "2(a - b) = -2d<BR>\n" );
document.write( "a - c = -2d<BR>\n" );
document.write( "2(b - c) = -2d<BR>\n" );
document.write( "(ii) <BR>\n" );
document.write( "(a - c)^2 = 4d^2<BR>\n" );
document.write( "4(b^2 - ac) = 4( (a+d)^2 - a(a+2d) ) = 4( a^2 + 2ad + d^2 - a^2 - 2ad ) = 4d^2<BR>\n" );
document.write( " </SPAN>\n" );
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