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# If p, q, r are in A.P., then pth,qth and rth terms of any G.P. are themselves inA.P.G.P.H.P.None of these

A
A.P.
B
None of these
C
H.P.
D
G.P.
Solution
Verified by Toppr

#### p, q and r are in A.Pi.e. 2q=p+rGeneral term of G.P is T(K)=ar(k−1)pth term is :- T(p)=ar(p−1)...(1)qth term is :- T(q)=ar(q−1)...(2)rth term is :- T(r)=ar(R−1)...(3)To prove that ;- T(p),T(q),T(r) are in G.PT(q)2=T(p).T(r)[ar(q−1)]2=ar(p−1).ar(R−1)a2ar2(q−1)=a2r(p−1)r(R−1)r2(q−1)=r(P+R−2)Taking only powers2(q−1)=P+R−22q−2=P+R−22q=P+RThis proves that pth,qth and rthterm are in G.P

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