If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of 2 4 + 1 3 4 n is 6 : 1 , then the third term from the beginning is:

Step-by-step solution

Given expansion is 2 4 + 1 3 4 n We know that general term of an expansion x + a n is T r + 1 = C r n x n - r a r ( 5 th term from beginning) T 4 + 1 = C 4 n ( 2 4 ) n - 4 · 1 3 4 4 ( 5 th term from end) We know that r th term from the end in a binomial expansion is T n - r + 2 from the beginning. T 5 ' = T n - 4 + 1 = C 4 n 1 3 4 n - 4 ( 2 4 ) 4 It is also given that the ratio of the fifth term from the beginning to the fifth term from the end is 6 : 1 . Now, T 5 T 5 ' = 6 1 ⇒ 2 n - 8 4 · 3 n -