8,12,18,... may represent a geometric progression (GP) where a=8 and r=1.5 and the series up to the nth term, where integer n>2, is:
a,ar,ar2,ar3,...,arn-1. The sum Sn=a(rn-1)/(r-1).
The sum of the interior angles of a polygon (n-gon) is 180(n-2)°.
Therefore if the angles form a geometric progression then:
Sn=a(rn-1)/(r-1)=180(n-2) for some integer n.
For a=8 and r=1.5:
8(1.5n-1)/0.5=16(1.5n-1)=180(n-2),
1.5n=11.25(n-2)+1=11.25n-21.5. This has no integer solutions for n.
So the given set of terms cannot be a GP. Neither do the terms form an arithmetic progression (AP).
Even if the series was 6,12,18,... (AP), n could not be an integer.
More information is needed.