Q. 215.0( 2 Votes )

# Find the sixth term in the expansion if the binomial coefficient of the third term from the end is 45.

Answer :

In the binomial expansion of , there are (n + 1) terms.

The third term from the end in the expansion of , is the third term from the beginning in the n expansion of .

The binomial coefficient of the third term from the end = ^{n}C_{2}

It is given that the binomial coefficient of the third tern from the end is 45.

Since, ^{n}C_{2} = 45

n^{2} - n - 90 = 0

(n – 10) (n + 9) = 0

Therefore, n = 10 (n cannot be negative)

Let T_{6} be the 6^{th} term in the binomial expansion of .Then

T_{6} = ^{n}C_{5}

Now, Put n = 10

T_{6} = T_{5 + 1} = ^{10}C_{5}

T_{5 + 1} =

T_{5 + 1} =

T_{5 + 1} =

Hence, the 6^{th} Term is

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