Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n , in the increasing powers of 1 3 4 be 6 4 : 1 . If the sixth term from the beginning is α 3 4 , then α i

Question

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n , in the increasing powers of 1 3 4 be 6 4 : 1 . If the sixth term from the beginning is &#945; 3 4 , then &#945; is equal to _______.

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Given, The ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n in the increasing powers of 1 3 4 be 6 4 : 1 Now according to given data we have, T 5 T n - 3 = C 4 n 2 1 / 4 n - 4 3 - 1 / 4 4 C n - 4 n 2 1 / 4 4 3 - 1 / 4 n - 4 = 6 4 1 &#8658; 2 n - 8 4 3 n - 8 4 = 6 1 / 4 &#8658; 6 n - 8 = 6 &#8658; n - 8 = 1 &#8658; n = 9 So, T 6 = C 5 9 2 1 / 4 4 3 - 1 / 4 5 = 84 3 4 Now comparing with T 6 = &#945; 3 4 , We get &#945; = 84

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n , in the increasing powers of 1 3 4 be 6 4 : 1 . If the sixth term from the beginning is α 3 4 , then α is equal to _______.

Correct answer

Step-by-step solution

More from Binomial Theorem

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n , in the increasing powers of 1 3 4 be 6 4 : 1 . If the sixth term from the beginning is &#945; 3 4 , then &#945; is equal to _______.

Correct answer

Step-by-step solution

More from Binomial Theorem

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of 2 4 + 1 3 4 n , in the increasing powers of 1 3 4 be 6 4 : 1 . If the sixth term from the beginning is α 3 4 , then α is equal to _______.