If the $p^{th},q^{th},$ and $r^{th}$ terms of an A.P. are in G.P., then common ratio of the G.P. is

$p^{th},q^{th},r^{th}$ terms of A.P. are 

$a+(p-1)d=x$             (1)

$a+(q-1)d=xR$        (2)

$a+(r-1)d=x{R}^2$     (3)

Where r is common ratio of G.P. 

Subtracting (2) from (3) and (1) from (2) and then dividing the former by the later, we have

$\frac{q-r}{p-q}=\frac{x{R}^2-xR}{xR-x}=R$