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

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Correct option is D

pth ,qth ,rth terms of A.P are a+(p−1)d=xa+(q−1)d=xRa+(r−1)d=xR2 Where R is common ratio of G.P Subtracting (3) from (2) and (2) from (1) and then dividing the formerby the later, we have q−rp−q=xR2−xRxR−xR2=R

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If the pth ,qth, and rth terms of an A.P. are in G.P. then common ratio of the G.P is

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