Question

Find the 6th term in the expansion of (4x/5-5/2x)^9

Answer 1

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Answer 2

The sixth term of the given binomial expansion is  $- \frac{5040}{x}$.

Step-by-step explanation:

The (r + 1)th term of the binomial expansion of $(a + x)^{n}$ is given by $^nC_{r}a^{(n -r)} x^{r}$.

Therefore, the 6th term of the binomial expansion of $(\frac{4x}{5} - \frac{5}{2x} )^{9}$ will be

$^9C_{5} (\frac{4x}{5} )^{(9 - 5)} (- \frac{5}{2x} )^{5}$

{Here, n is represented by 9, r is represented by 5 and a is represented by $\frac{4x}{5}$ and x is represented by $- \frac{5}{2x}$}

= $126 \times (\frac{4}{5} )^{4} \times (- \frac{5}{2} )^{5} \times \frac{1}{x^{1} }$

= $- 5040 \times \frac{1}{x}$

=  $- \frac{5040}{x}$

Therefore, the sixth term of the given binomial expansion is  $- \frac{5040}{x}$. (Answer)