Will upvote

4,7,12,19,31, ... 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.