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Standard XII
Mathematics
Sum of n Terms
Question
If a,b,c are in AP and x,y,z are in GP, prove that
x
b
−
c
.
y
c
−
a
.
z
a
−
b
=
1
Open in App
Solution
Verified by Toppr
Given
a
,
b
,
c
are in
A
.
P
⟹
2
b
=
a
+
c
And also
x
,
y
,
z
are in
G
.
P
⟹
y
=
√
x
z
L
H
S
=
x
b
−
c
.
y
c
−
a
.
z
a
−
b
=
x
b
−
c
.
z
a
−
b
.
(
√
x
z
)
c
−
a
=
x
b
−
c
.
z
a
−
b
.
x
c
−
a
2
.
z
c
−
a
2
=
x
2
b
−
(
a
+
c
)
2
z
2
b
−
(
a
+
c
)
2
=
x
0
.
z
0
=
1
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Similar Questions
Q1
If a,b,c are in AP and x,y,z are in GP, prove that
x
b
−
c
.
y
c
−
a
.
z
a
−
b
=
1
View Solution
Q2
If a b and c are in GP and
a
1
/
x
=
b
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/
y
=
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/
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, prove that x, y and z are in AP.
View Solution
Q3
If a,b,c are in AP whereas x,y,z are in GP , what is the value of
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)
.
y
(
c
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a
)
.
z
(
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?
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Q4
If
a
,
b
,
c
are in AP and
b
,
c
,
d
are in GP and
1
c
,
1
d
,
1
e
are in AP, prove that
a
,
c
,
e
are in GP.
View Solution
Q5
If a, b, c are in G.P. and a
1
/x
= b
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/y
= c
1
/z
, then xyz are in
(a) AP
(b) GP
(c) HP
(d) none of these
View Solution