Let he sum of the coefficient of first three terms in the expansion of x - 3 x 2 n ; x = 0 , n ∈ N be 376 . Then, the coefficient of x 4 is equal to:

Step-by-step solution

We know that general term in the expansion of x - 3 x 2 n is given by, T r + 1 = C r n x n - r - 3 x 2 r = - 1 r × C r n 3 r   x n - r - 2 r T r + 1 = - 1 r × C r n 3 r   x n - 3 r . . . . . . . . . . . . . . . 1 So, T 1 = T 0 + 1 =   C 0 n 3 0   x n = x n T 2 = - 1 ×   C 1 n 3 1   x n - 3 T 3 = C 2 n 3 2   x n - 6 Now given sum is 1 -   C 1 n · 3 +   C 2 n · 3 2 = 376 ⇒ 1 - 3 n + n n - 1 2 · 9 = 376 ⇒ 1 - 3 n + n 2 - n 2 ·