the first blank has the options coverges and diverges
the second blank has the options arithmetic and geometric and the absolute value of the common ration is less than 1 and geometric and the absolute value of the common ration is greater than 1.
This series diverges ( we have larger and larger negatives as terms are added )
Only geometric series have common ratios......arithmetic series have a common difference
The common difference is
15/2 - 16
15/2 - 32/2 =
Tha absolute value of this difference > 1