T4 = 12 C3 ( x ) 9 ( -2y ) 3
Or T4 = -1760 x 9 y 3 Middle term in the expansion of ( a + b ) n Case 1 : “ n ” is even , Total term is expansion : n + 1 à Odd Middle term = ( n / 2 + 1 ) th
We Can now find the middle term using the general term formula , Tr + 1 = n Cr a n – r b r
Case 2 : “ n ” is odd , total term in expansion : n + 1 à Even There will be two Middle terms = (( n + 1 )/ 2 ) th
& (( n + 1 )/ 2 + 1 ) th terms
We can now find the middle term using the general term formula
Tr + 1 = n Cr a n – r b r
Numerical : Find the middle terms in the expansions of ( x / 3 + 9y ) 10 Solution : in this case , a = x / 3 , b = 9y & n = 10 Since n = 10 , number of terms in the expansion will be 11 . Middle terms will be ( 11 + 1 )/ 2 = 6 To find T6 , we need to put r = 5 in the formula Tr + 1 = n Cr a n – r b r
T5 + 1 = 10 C5 ( x / 3 ) 10-5 ( 9y ) 5
Or T6 = 61236x 5 y 5