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Question

- A.P.
- G.P.
- H.P.
- None of these

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Solution

Verified by Toppr

p, q and r are in A.P

i.e. 2q=p+r

General 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.P

T(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 powers

2(q−1)=P+R−2

2q−2=P+R−2

2q=P+R

This proves that pth,qth and rth

term are in G.P

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