Question

If the 4^th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are ______.

Options

• 2, 6

• `1/2, 6`

• `1/2, 5`

• 2, 5

Answer 1

If the 4^th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are `underlinebb(1/2, 6)`.

Explanation:

T₄ = `""^nC_3(ax)^(n-3)(1/x)^3`

= `""^nC_3a^(n-3)x^(n-6) = 5/2` ...(Given)

∴ n – 6 = 0

⇒ n = 6

T₄ = `""^6C_3a^(6 - 3) = 5/2`

⇒ a³ = `1/8 = (1/2)^3`

⇒ a = `1/2`

⇒ a = `1/2`, n = 6