Will upvote

4,7,12,19, does this classify as a arithmetic, geometric, or neither

To find if a series is either geometric or arithmetic:
it must satisfy this property:

Arithmetic:

a(n+1) - a(n) = const

Geometric:

a(n+1)/a(n) = const

In your case:

r1 = 7 -4 = 3

r2 = 12 - 7 = 5

r1 != r2  (not arirthmetic)

Geometric check:

r1 = 7/4

r2 = 12/7

r1 != r2  (not Geometric)

so neither.