The sequence \(a_1, a_2, a_3, \ldots , a_n, \ldots\) is such that \(a_n=\dfrac{a_{n-1}+a_{n-2}}2\) for all \(n \ge 3.\) If \(a_3=4\) and \(a_5=20,\) what is the value of \(a_6 ?\)

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

[spoiler]OA=E[/spoiler]

Source: Official Guide