Question

Find the 7th term in the expansion of ${\left(\frac{4x}{5}+\frac{5}{2x}\right)}^8$.

Answer 1

We need to find the 7th term in the given expression.

$\because T_7=T_{6+1}$

$$\begin{gathered} \therefore T_7=T_{6+1} \\ ={}^{8}C_6{\left(\frac{4x}{5}\right)}^{8-6}{\left(\frac{5}{2x}\right)}^6 \\ =\frac{8\times 7\times 4\times 4\times 125\times 125}{2\times 1\times 25\times 64}{x}^2\left(\frac{1}{x^6}\right) \\ =\frac{4375}{x^4} \end{gathered}$$