document.write( "Question 1110010: The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the sequence is arithmetic then X(y-z) + Y(z-x) + Z(x-y)=0.\r
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Algebra.Com's Answer #725012 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "let p=x, q=y, and r=z.  Then the problem is:\r\n" );
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\n" ); document.write( "The pth, qth, and rth terms of a sequence are X,Y,Z respectively. Show that
\n" ); document.write( "if the sequence is arithmetic then X(q-r) + Y(r-p) + Z(p-q)=0.
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document.write( "Let the sequence be arithmetic, with first term a \r\n" );
document.write( "and common difference d, then by the formula for nth term, \r\n" );
document.write( "we have these three equations:\r\n" );
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document.write( "Solve the first and second equations for d\r\n" );
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document.write( "Solve the first and third equations for d\r\n" );
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document.write( "Since both expressions equal d, they are equal to each other\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "Edwin

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