If the fifth term of the expansion $\Big(\text{a}^{\frac{2}{3}}+\text{a}^{-1}\Big)^{\text{n}}$ does not contain 'a'. Then n is equal to:

Question

Aicharya · Accepted Answer

Solution: $\text{T}_{5}=\text{T}_{4+1}$ $={^\text{n}}\text{C}_{\text{4}}\big(\text{a}^{\frac{2}{3}}\big)^{\text{n-4}}(\text{a}^{-1})^{4}$ $={^\text{n}}\text{C}_{\text{4}}\ \text{a}^{\big(\frac{2\text{n}-8}{3}-4\big)}$ For this term to be independent of a, we must have $\frac{2\text{n}-8}{3}-4=0$ $\Rightarrow 2\text{n}-20=0$ $\Rightarrow \text{n}=10$

If the fifth term of the expansion \(\Big(\text{a}^{\frac{2}{3}}+\text{a}^{-1}\Big)^{\text{n}}\) does not…

Solution