what sequence is 5,7,12,20,31? is it Arithmetic, Geometric, or Neither

Thanks for the A2A.

The answer is neither.

Cheers!

Using sequence differences, you have this:
 5, 7, 12, 20, 31
   2,  5,  8,  11
      3,  3,  3

From the above, we can formulate a "closed form" as follows:

a_n = 1/2 (3 n^2 - 5 n + 12), which will give you each term in your sequence as follows: 

5, 7, 12, 20, 31, 45, 62, 82, 105, 131, 160, 192, 227, 265, 306, 350, 397, 447, 500, ....etc.

If arithmetic....the difference between succesive terms would be  constant....this clearly isn't true

If geometric.....then this must be true

7/5  = 12/7   

1.4  = 1.7142857  

Not true....so.... not geometric, either