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If \(l^{th}\), \(m^{th}\), \(n^{th}\) terms of an \(A.P.\) are \(x\), \(y\), \(z\) respectively, then show that \((x - y)n + (y - z)l + (z - x)m = 0\)
 
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This is a self-assessment task. Solve this question and assess the solution steps after the test's completion on your own.