Final answer:
The sum of the provided arithmetic series cannot be calculated as it is infinite and tends to negative infinity. To sum a finite section of the series, the formula for an arithmetic series sum is ½n(a1 + an), but specific numbers of terms and values are needed.
Step-by-step explanation:
The sum of an arithmetic series can be calculated using the formula S = ½n(a1 + an), where S is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term. However, the series provided is infinite and negative, which means it does not have a sum in the conventional sense as it tends to negative infinity. To find the sum of a finite number of terms in the series, we would need the number of terms and the last term considered. Rules for addition with negative numbers and arithmetic series apply to such computations. This involves adding negative numbers which always results in a more negative sum, consistent with the rule that when two negative numbers are added, the answer has a negative sign. The sequence presented: 0, -3, -6, -9, ... shows a constant difference of -3, which is the common difference of the arithmetic series.