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Question
If the
p
t
h
,
q
t
h
,
and
r
t
h
terms of an A.P. are in G.P., then common ratio of the G.P. is
A
q
2
p
r
B
p
r
C
p
+
q
q
+
r
D
p
−
q
q
−
r
Medium
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Solution
Verified by Toppr
Correct option is D)
p
t
h
,
q
t
h
,
r
t
h
terms of A.P. are
a
+
(
p
−
1
)
d
=
x
(1)
a
+
(
q
−
1
)
d
=
x
R
(2)
a
+
(
r
−
1
)
d
=
x
R
2
(3)
Where r is common ratio of G.P.
Subtracting (2) from (3) and (1) from (2) and then dividing the former by the later, we have
p
−
q
q
−
r
=
x
R
−
x
x
R
2
−
x
R
=
R
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