what happens to the variance of the sampling distribution of the sample means when the sample size increases

The variance of the sampling distribution of the sample means is given as,

$var(\bar x_i)={\sigma^2\over n}$ where $\sigma^2$ is the population variance and $n$ is the sample size. Clearly, the sample size is on the denominator side of this formula. Therefore, when the sample size is increased the variability of each sampling distribution decreases.