2021-II-36

I must be true. Since $p$, $q$, $r$ and $s$ is a geometric sequence, then we have

$\begin{array}{rcl}{\displaystyle \frac{q}{p}}& =& {\displaystyle \frac{s}{r}}\\ ps& =& qr\end{array}$

II may not be true. For the geometric sequence $p=1$, $q=2$, $r=4$ and $s=8$, it is not true that $p+s=q+r$.

III may not be true. For the geometric sequence $p=1$, $q={\displaystyle \frac{1}{2}}$, $r={\displaystyle \frac{1}{4}}$ and $s={\displaystyle \frac{1}{8}}$, it is not true that $p<q<r<s$.