RU-ALLRUSSIAN 1983 Problem 7

$\mathrm{a}_{\mathrm{n}}$ is the last digit of $[10^{n / 2}]$ . Is the sequence $\mathrm{a}_{\mathrm{n}}$ periodic? $\mathrm{b}_{\mathrm{n}}$ is the last digit of $[2^{n / 2}]$ . Is the sequence $\mathrm{b}_{\mathrm{n}}$ periodic?