Solve
Study
Textbooks
Guides
Use app
Login
Question
If the
p
th,
q
th and
r
th terms of a GP are
a
,
b
,
c
respectively. Prove that
a
q
β
r
b
r
β
p
c
p
β
q
=
1
Easy
Open in App
Solution
Verified by Toppr
Formula,
a
n
β
=
a
r
n
β
1
a
=
a
r
p
β
1
β
a
q
β
r
=
(
a
r
p
β
1
)
q
β
r
........(1)
b
=
a
r
q
β
1
β
b
r
β
p
=
(
b
r
q
β
1
)
r
β
p
........(2)
c
=
a
r
r
β
1
β
c
p
β
q
=
(
c
r
r
β
1
)
p
β
q
........(3)
multiplying (1),(2) and (3), we get,
a
q
β
r
b
r
β
p
c
p
β
q
=
(
a
r
p
β
1
)
q
β
r
(
b
r
q
β
1
)
r
β
p
(
c
r
r
β
1
)
p
β
q
=
a
(
p
+
q
+
r
β
p
β
q
β
r
)
r
(
p
q
+
q
r
+
r
p
+
p
+
q
+
r
β
p
q
β
q
r
β
r
p
β
p
β
q
β
r
)
=
a
0
r
0
=
1
Hence proved.
Was this answer helpful?
0
0
Similar questions
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
β
r
b
r
β
p
c
p
β
q
=
1
.
Medium
View solution
>
If the
p
t
h
,
q
t
h
a
n
d
r
t
h
terms of a G.P. are a,b and c, respectively. Prove that
Β Β Β Β
a
q
β
r
b
r
β
p
c
p
β
q
=
1
.
Hard
View solution
>
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
β
r
b
r
β
p
c
p
β
q
=
1
.
Hard
View solution
>
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
Hard
View solution
>
If
p
t
h
,
q
t
h
,
r
t
h
and
s
t
h
terms of an
A
.
P
are in
G
.
P
then
p
β
q
,
q
β
r
,
r
β
s
are in
G
.
P
.
Medium
View solution
>