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Byju's Answer
Standard XII
Mathematics
Multinomial Expansion
If in the exp...
Question
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
(c) 8, 16
(d) none of these
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Solution
(b) 7, 14
Coefficients
of
the
5
th
,
6
th
and
7
th
terms
in
the
given
expansion
are
C
4
n
,
C
5
n
and
C
6
n
These
coefficients
are
in
A
P
.
Thus
,
we
have
2
C
5
n
=
C
4
n
+
C
6
n
On
dividing
both
sides
by
C
5
n
,
w
e
g
e
t
:
2
=
C
4
n
C
5
n
+
C
6
n
C
5
n
⇒
2
=
5
n
-
4
+
n
-
5
6
⇒
12
n
-
48
=
30
+
n
2
-
4
n
-
5
n
+
20
⇒
n
2
-
21
n
+
98
=
0
⇒
(
n
-
14
)
(
n
-
7
)
=
0
⇒
n
=
7
and
14
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