#### Answer

a) $\{10,5,2.5,1.25\}$
b) $h_n = 0.5^n(20)$

#### Work Step by Step

a) $h_0 = 20$; $h_n = r(h_{n-1})$
$h_n = 0.5h_{n-1}$
$h_1 = 0.5h_0 = 10$
$h_2 = 0.5h_1 = 5$
$h_3 = 0.5h_2 = 2.5$
$h_4 = 0.5h_3 = 1.25$
b) We need to multiply by a factor of $r$ a total of $n$ times to the original value of $h_0$.
$h_n = r^nh_0 = 0.5^n(20)$