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Standard XII
Maths
Question
If the
p
t
h
,
q
t
h
and
r
t
h
terms of a G.P. are a, b and c, respectively. Prove that
a
q
−
r
b
r
−
p
c
p
−
q
=
1
.
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Solution
Verified by Toppr
L
e
t
f
i
r
s
t
t
e
r
m
A
a
n
d
c
o
m
m
o
n
d
i
f
f
e
r
e
n
c
e
(
R
)
t
p
=
a
t
q
=
b
t
r
=
c
∣
∣ ∣ ∣
∣
G
.
P
.
t
p
=
A
R
p
−
1
=
a
t
q
=
A
R
q
−
1
=
b
t
r
=
A
R
r
−
1
=
c
t
h
e
n
a
q
−
r
.
b
r
−
p
.
c
p
−
q
{
A
R
p
−
1
}
q
−
r
{
A
R
q
−
1
}
r
−
p
{
A
R
r
−
1
}
p
−
q
A
(
q
−
r
+
r
−
p
+
p
−
a
)
.
R
{
(
p
−
1
)
(
q
−
1
)
+
(
q
−
1
)
(
r
−
p
)
+
(
r
−
1
)
(
p
−
q
)
}
A
∘
.
R
∘
=
1
∴
a
q
−
r
.
b
r
−
p
.
c
p
−
q
=
1
P
r
o
v
e
d
.
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