Find the $20^{t h}$ term in the binomial expansion of $(1 + x)^{20}$ when $x = - 5$

$- 20 \times 5^{19}$

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$20 \times 5^{20}$

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$- 20 \times 5^{20}$

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$20 \times 5^{19}$

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Solution

The correct option is A
$- 20 \times 5^{19}$

We want to find the $20^{t h}$ term or $T_{20}$
We know $T_{r + 1} =^{n} C_{r} x^{n - r} y^{r}$ in the expansion of $(x + y)^{n}$
$T_{r + 1}$ in the expansion of $(1 - x)^{n} i s^{n} C_{r} {(- x)}^{r}$
$\Rightarrow T_{20} = (- 1)^{19} \cdot^{20} C_{19} \cdot x^{19}$ (Because r=19 in this case)
= $- 20 \times 5^{19}$

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