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

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 = nC2

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

Since, nC2 = 45

n2 - n - 90 = 0

(n – 10) (n + 9) = 0

Therefore, n = 10 (n cannot be negative)

Let T6 be the 6th term in the binomial expansion of .Then

T6 = nC5

Now, Put n = 10

T6 = T5 + 1 = 10C5

T5 + 1 =

T5 + 1 =

T5 + 1 =

Hence, the 6th Term is

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