Answer
(a)
Common ratio: $r=\frac{1}{4}$
(b)
$a_n=12(\frac{1}{4})^{n-1}$
$a_n=48(\frac{1}{4})^{n}$
(c)
$a_{10}=\frac{3}{4^8}=0.0000457763671875$
Work Step by Step
(a)
$\frac{a_2}{a_1}=\frac{3}{12}=\frac{1}{4}$
$\frac{a_3}{a_2}=\frac{\frac{3}{4}}{3}=\frac{1}{4}$
Common ratio: $r=\frac{1}{4}$
(b)
$a_n=ar^{n-1}$
$a_n=12(\frac{1}{4})^{n-1}$
$a_n=48(\frac{1}{4})^{n}$
(c)
$a_{10}=12(\frac{1}{4})^{10-1}=\frac{12}{4^9}=\frac{3}{4^8}=0.0000457763671875$
