How are the $p$th, $q$th and $r$th terms of an AP related?

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The \(p\)th term of a progression is \(P\), the \(q\)th term is \(Q\), and the \(r\)th term is \(R\). Show that, if the progression is arithmetical, \[P(q-r)+Q(r-p)+R(p-q)=0\] and that, if it is geometrical, \[(q-r)\log P+(r-p)\log Q+(p-q)\log R=0.\]