Solve
Study
Textbooks
Guides
Use app
Login
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
β
r
b
r
β
p
c
p
β
q
=
1
.
Medium
Open in App
Solution
Verified by Toppr
Let
A
be the first term and
R
be the common ratio. Then,Β
a
=
p
t
h
term
=
A
R
(
p
β
1
)
b
=
q
t
h
term
=
A
R
(
q
β
1
)
c
=
r
t
h
term
=
A
R
(
r
β
1
)
Substituting values of
a
,
b
&
c
, we get,
a
(
q
β
r
)
.
b
(
r
β
p
)
.
c
(
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
)
=
A
(
q
β
r
)
R
(
p
β
1
)
(
q
β
r
)
.
A
(
r
β
p
)
R
(
q
β
1
)
(
r
β
p
)
.
A
(
p
β
q
)
R
(
r
β
1
)
(
p
β
q
)
=
A
0
R
0
=
1
Was this answer helpful?
0
0
Similar questions
If the
4
t
h
,
1
0
t
h
and
1
6
t
h
terms of a G.P. are
x
,
y
and
z
, respectively. Prove that
x
,
y
,
z
are in G.P.Β
Medium
View solution
>
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
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
>
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
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
>