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Byju's Answer
Standard XI
Mathematics
Binomial Coefficients
If the 5th,...
Question
If the
5
t
h
,
6
t
h
,
and
7
t
h
term in the expansion of
(
1
+
y
)
n
are in A.P. then find the value of
n
.
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Solution
The coefficients of the
5
t
h
,
6
t
h
and
7
t
h
terms are
n
C
4
,
n
C
5
,
n
C
6
Since the coefficients of the
5
t
h
,
6
t
h
and
7
t
h
terms are in
A
P
. we have,
n
C
5
−
n
C
4
=
n
C
6
−
n
C
5
⇒
n
!
5
!
(
n
−
5
)
!
−
n
!
4
!
(
n
−
4
)
!
=
n
!
6
!
(
n
−
6
)
!
−
n
!
5
!
(
n
−
5
)
!
⇒
1
120
(
n
−
5
)
!
−
1
24
(
n
−
4
)
(
n
−
5
)
!
=
1
720
(
n
−
6
)
!
−
1
120
(
n
−
5
)
(
n
−
6
)
!
⇒
1
24
(
n
−
5
)
!
[
1
5
−
1
n
−
4
]
=
1
120
(
n
−
6
)
!
[
1
6
−
1
n
−
5
]
⇒
1
(
n
−
5
)
[
n
−
4
−
5
5
(
n
−
4
)
]
=
1
5
[
n
−
5
−
6
6
(
n
−
5
)
]
⇒
n
−
9
n
−
4
=
n
−
11
6
⇒
n
2
−
21
n
+
98
=
0
⇒
n
=
7
,
14
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0
Similar questions
Q.
If in the expansion of
(
1
+
y
)
n
, the coefficient of
5
t
h
,
6
t
h
and
7
t
h
terms are in A.P., then
n
is equal to:
Q.
If the
5
t
h
,
6
t
h
&
7
t
h
term in the expansion of
(
1
+
y
)
n
are in AP then find n.
Q.
If the coefficients of 5th , 6th and 7th terms in the expansion of
(
1
−
x
)
n
are in A.P then find the value of n.
Q.
In the binomial expansion of
(
1
+
y
)
n
, where
n
is a natural number, the coefficients of the
5
t
h
,
6
t
h
and
7
t
h
terms are in A.P, find
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Q.
If in the expansion of (1 + y)
n
, the coefficients of 5th, 6th and 7th terms are in A.P., then n is equal to
(a) 7, 11
(b) 7, 14
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(d) none of these
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