Fizzy AP - GP

Algebra

Let $a, b \in R^{+}.$

$a, A_{1}, A_{2}, b$ is an arithmetic progression.
$a, G_{1}, G_{2}, b$ is a geometric progression.

Which of the following must be true?

A_{2}G_{1} \geq G_{2}A_{1}

A_{1}G_{2} \geq G_{1}A_{2}

A_{1}A_{2} \geq G_{1}G_{2}

A_{1}A_{2} > G_{1}G_{2}