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Byju's Answer
Standard XII
Mathematics
Common Ratio
If pth, qth a...
Question
If p
th
, q
th
and r
th
terms of a G.P. are x, y, z respectively, then write the value of x
q
− r
y
r
− p
z
p
− q
.
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Solution
Let us take a G.P. whose first term is
A
and common ratio is R.
According
to
the
question
,
we
have
:
A
R
p
-
1
=
x
A
R
q
-
1
=
y
A
R
r
-
1
=
z
∴
x
q
-
r
y
r
-
p
z
p
-
q
=
A
q
-
r
×
R
p
-
1
q
-
r
×
A
r
-
p
×
R
q
-
1
r
-
p
×
A
p
-
q
×
R
r
-
1
p
-
q
=
A
q
-
r
+
r
-
p
+
p
-
q
×
R
p
r
-
p
r
-
q
+
r
+
r
q
-
r
+
p
-
p
q
+
p
r
-
p
-
q
r
+
q
=
A
0
×
R
0
=
1
∴
x
q
-
r
y
r
-
p
z
p
-
q
=
1
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0
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