Question 1083080
a(n) = a(r^(n-1))

a(3) = a(r^2) = 12.

a(4) = a(r^3) = 8.

a(4)/(a(3)) = r = 8/12 = 2/3.

a(4) = a(2/3)^3 = 8.

       a = 27.

So a(n) = 27*(2/3)^(n-1).

using 1/(1-r) =lim n--->inf( 1 +r^1 +r^2 + r^3 + ... r^n),  if |r|<1

Sum(a(n))) = 27/(1-2/3)) = 27/(1/3) = 81.

@natolino_