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Question
If
p
t
h
,
q
t
h
,
r
t
h
and
s
t
h
, terms of an A.P are in G.P, then the show that
(
p
−
q
)
,
(
q
−
r
)
,
(
r
−
s
)
are also in G.P ?
Medium
Open in App
Solution
Verified by Toppr
∵
a
p
=
a
+
(
p
−
1
)
d
;
a
q
=
a
+
(
q
−
1
)
d
;
a
r
=
a
+
(
r
−
1
)
d
;
a
s
=
a
+
(
s
−
1
)
d
;
A
/
Q
p
t
h
,
q
t
h
,
r
t
h
,
s
t
h
t
e
r
m
a
r
e
i
n
G
.
P
∴
a
p
a
q
=
a
q
a
r
=
a
r
a
s
f
o
r
a
p
a
q
=
a
q
a
r
⇒
a
p
a
q
−
1
=
a
q
a
r
−
1
⇒
a
p
a
q
=
a
q
−
a
p
a
r
−
a
q
p
u
t
t
i
n
g
t
h
e
v
a
l
u
e
o
f
t
e
r
m
w
e
g
e
t
⇒
a
p
a
q
=
(
a
+
(
q
−
1
)
d
)
−
(
a
+
(
p
−
1
)
d
)
(
a
+
(
r
−
1
)
d
)
−
(
a
+
(
q
−
1
)
d
)
=
p
−
q
q
−
r
⟶
(
1
)
s
i
m
i
l
a
r
l
y
f
o
r
a
q
a
r
=
a
r
a
s
⇒
a
q
a
r
=
q
−
r
r
−
s
⟶
(
2
)
f
r
o
m
(
1
)
a
n
d
(
2
)
w
e
c
o
m
e
t
o
k
n
o
w
(
p
−
q
)
,
(
q
−
r
)
a
n
d
(
r
−
s
)
a
r
e
i
n
G
.
P
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