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Question
If
p
t
h
,
q
t
h
and
r
t
h
term of a G.P. are
x
,
y
and
z
respectively prove that :
x
a
β
r
x
y
r
β
p
x
z
p
β
q
=
1
.
Easy
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Solution
Verified by Toppr
Given,
a
r
p
β
1
=
x
a
r
q
β
1
=
y
a
r
r
β
1
=
z
β
(
a
r
p
β
1
)
q
β
r
=
x
q
β
r
β
(
a
r
q
β
1
)
r
β
p
=
y
r
β
p
β
(
a
r
r
β
1
)
p
β
q
=
z
p
β
q
x
q
β
r
y
r
β
p
z
p
β
q
=
(
a
r
p
β
1
)
q
β
r
(
a
r
q
β
1
)
r
β
p
(
a
r
r
β
1
)
p
β
q
x
q
β
r
x
y
r
β
p
x
z
p
β
q
=
a
(
p
+
q
+
r
β
p
β
q
β
r
)
r
(
p
q
+
q
r
+
r
p
+
p
+
q
+
r
β
q
p
β
r
q
β
p
r
β
p
β
q
β
r
)
β
x
q
β
r
x
y
r
β
p
x
z
p
β
q
=
a
0
r
0
β΄
x
q
β
r
x
y
r
β
p
x
z
p
β
q
=
1
Hence proved.
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