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 = 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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