Question

If the 4^th term in the expansion of $\left( ax + \frac{1}{x} \right)^{n}$ is $\frac{5}{2}$, then the value of a & n are –

• A. $\frac{1}{2}$, 6
• B. 1, 3
• C. $\frac{1}{2}$, $\frac{1}{3}$
• D. Can not be found

Answer 1

Answer: (A)

$\frac{1}{2}$, 6

Answer 2

T₄ = ⁿC₃ (ax)^n–3 $\left( \frac{1}{x} \right)^{3}$ = $\frac{5}{2}$ (independent of x)

\ x^n–6 = x⁰

i.e. n = 6

& ⁶C₃ a³ = $\frac{5}{2}$

Ž a = $\frac{1}{2}$