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Question
If p, q, r are in A.P., then
p
t
h
,
q
t
h
and
r
t
h
terms of any G.P. are themselves in
A
A.P.
B
G.P.
C
H.P.
D
None of these
Hard
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Solution
Verified by Toppr
Correct option is B)
p, q and r are in A.P
i.e.
2
q
=
p
+
r
General term of G.P is
T
(
K
)
=
a
r
(
k
β
1
)
p
t
h
term is :-
T
(
p
)
=
a
r
(
p
β
1
)
.
.
.
(
1
)
q
t
h
term is :-
T
(
q
)
=
a
r
(
q
β
1
)
.
.
.
(
2
)
r
t
h
term is :-
T
(
r
)
=
a
r
(
R
β
1
)
.
.
.
(
3
)
To prove that ;-
T
(
p
)
,
T
(
q
)
,
T
(
r
)
are in G.P
T
(
q
)
2
=
T
(
p
)
.
T
(
r
)
[
a
r
(
q
β
1
)
]
2
=
a
r
(
p
β
1
)
.
a
r
(
R
β
1
)
a
2
a
r
2
(
q
β
1
)
=
a
2
r
(
p
β
1
)
r
(
R
β
1
)
r
2
(
q
β
1
)
=
r
(
P
+
R
β
2
)
Taking only powers
2
(
q
β
1
)
=
P
+
R
β
2
2
q
β
2
=
P
+
R
β
2
2
q
=
P
+
R
This proves that
p
t
h
,
q
t
h
and
r
t
h
term are in G.P
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