$a^2$, $b^2$, and $c^2$ are in arithmetic progression

$a$, $b$, and $c$ are in arithmetic progression

$a^2$, $b^2$, and $c^2$ are in geometric progression

$\frac{1}{a}$, $\frac{1}{b}$, and $\frac{1}{c}$ are in arithmetic progression