Suppose 28 - p , p , 70 - α , α are the coefficient of four consecutive terms in the expansion of ( 1 + x ) n . Then the value of 2 α - 3 p equals

Step-by-step solution

Given, 28 - p , p , 70 - α , α are the coefficient of four consecutive terms in the expansion of ( 1 + x ) n So, C r n = 28 - p , C r + 1 n = p , C r + 2 n = 70 - α & C r + 3 n = α ⇒ C r n + C r + 1 n = 28 & C r + 2 n + C r + 3 n = 70 ⇒ C r + 1 n + 1 = 28 & C r + 3 n + 1 = 70 We know that, C 2 8 = 28 or C 1 28 = 28 , Now on comparing with C r + 1 n + 1 = 28 we get, n , r = 7 , 1 or n , r = 27 , 0 Now, checking with C r + 3 n + 1 = 70 we get, n , r = 7 , 1 So, p = C 2 7 = 21 and α = C 4 7 = 35 Hence, the value of 2