Question

a3=(ar)2=24/a6=(ar)5=192

Answer 1

It is ar^n-1 = (6)(2)^10 - 1 = 6 * 2^9

Answer 2

$a3 = a {r}^{2} = 24....(1) \\ a6 = a {r}^{5} = 192....(2) \\ dividing \: (2) \: by \: (1) \\ \frac{a {r}^{2} }{a {r}^{5} } = \frac{192}{24} \\ {r}^{2} = 8 \\ r = \sqrt{8} = 2 \sqrt{2} \\ = > a {r}^{2} = 24 \\ = > a \times 8 = 24 \\ = > a = 3$