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Question

If p, q, r are in A.P., then pth,qth and rth terms of any G.P. are themselves in
  1. A.P.
  2. G.P.
  3. H.P.
  4. 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.P
i.e. 2q=p+r
General term of G.P is T(K)=ar(k1)
pth term is :- T(p)=ar(p1)...(1)
qth term is :- T(q)=ar(q1)...(2)
rth term is :- T(r)=ar(R1)...(3)
To prove that ;- T(p),T(q),T(r) are in G.P
T(q)2=T(p).T(r)
[ar(q1)]2=ar(p1).ar(R1)
a2ar2(q1)=a2r(p1)r(R1)
r2(q1)=r(P+R2)
Taking only powers
2(q1)=P+R2
2q2=P+R2
2q=P+R
This proves that pth,qth and rth
term are in G.P

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