WAEC 2023 · Paper 1 · Q37

Find the coefficient of the $6^{\text{th}}$ term in the binomial expansion of $\left(1 - \dfrac{2x}{3}\right)^{10}$ in ascending powers of $x$ .

Worked solution (try it first)

The $6^{\text{th}}$ term has $r = 5$ : $^{10}C_5 \left(-\dfrac{2x}{3}\right)^5$ .
$^{10}C_5 = 252$ and $\left(-\frac{2}{3}\right)^5 = -\frac{32}{243}$ .
Multiply: $252 \times \left(-\frac{32}{243}\right) = -\frac{8064}{243}$
$= -\frac{896}{27}$ .
So the term is $-\dfrac{896x^5}{27}$ , option D.