Relation between CTFT and DTFT
Your sequence simply is a sampled version of the continuous signal $x(t)$. So

$$x_d(n)=x(nT),\quad T=\frac{1}{50}$$

The relation between the CTFT of $x(t)$ and the DTFT of $x_d(n)$ is that the DTFT is the sum of shifted versions of the CTFT. The spectra are shifted by the sampling frequency. That's the reason for aliasing.