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Question
Mathematics
If p, q, r are in A.P. and x, y, z are in G.P. then xq-r . y r-p.zp-q is equal to
Q. If
p
,
q
,
r
are in A.P. and
x
,
y
,
z
are in G.P. then
x
q
−
r
.
y
r
−
p
.
z
p
−
q
is equal to
2556
194
Sequences and Series
Report Error
A
1
47%
B
xyz
25%
C
x + y + z
16%
D
p+ q + r.
13%
Solution:
Since
p
,
q
,
r
are in
A
.
P
.
∴
2
q
=
p
+
r
...
(
i
)
Since
x
,
y
,
z
are in
G
.
P
.
Let
y
=
x
R
,
z
=
x
R
2
, where
R
is the ratio of the
G
.
P
.
∴
x
q
−
r
(
x
R
)
r
−
p
(
x
R
2
)
p
−
q
=
x
q
−
r
+
r
−
p
+
p
−
q
R
r
−
p
+
2
p
−
2
q
=
x
0
R
r
+
p
−
2
q
=
x
0
R
0
=
1
⋅
1
=
1
[By
(
1
)
]