Question

6. The middle term in the expansion of
(1-3n+3n²_ x 3)⁶ is
​

Answer 1

The middle term in the expansion of (1−3x+3x

2

−x

3

)

2n

is

MEDIUM

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ANSWER

Given, (1−3x+3x

2

−x

3

)

2n

=[(1−x)

3

]

2n

=(1−x)

6n

Middle term =

2

N

+1

=

2

6n

+1

=(3n+1)

th

term

Now consider the following,

T

r+1

=

n

C

r

a

n−r

b

r

...(i)

Where T represents the term

Here the middle term is the (3n+1)

th

term.

Hence, r+1=3n+1

r=3n

Substituting in (i), we get

(−1)

3n

6n

C

3n

1

6n−3n

x

3n

=(−1)

3n

6n

C

3n

x

3n

=

6n

C

3n

(−x)

3n