Find the 13th term in the expansion of

To find: $13^{\text {th }}$ term in the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}$

Formula used: (i) ${ }^{n} C_{r}=\frac{n !}{(n-r) !(r) !}$

(ii) $T_{r+1}={ }^{n} C_{r} a^{n-r} b^{r}$

For $13^{\text {th }}$ term, $r+1=13$

$\Rightarrow r=12$

$\ln ,\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}$

$13^{\text {th }}$ term $=T_{12+1}$

$\Rightarrow{ }^{18} C_{12}(9 x)^{18-12}\left(-\frac{1}{3 \sqrt{x}}\right)^{12}$

$\Rightarrow \frac{18 !}{12 !(18-12) !}(9 x)^{6}\left(-\frac{1}{3 \sqrt{x}}\right)^{12}$

$\Rightarrow 18564\left(531441 x^{6}\right)\left(\frac{1}{531441 x^{6}}\right)$

$\Rightarrow 18564$