546.
Let's make a step-by-step explanation in order to understand how we achieved this answer.
Let's unravel the series first:
-3, 9, -27, 81, -243, 729
As we can notice, this series is a geometric series wherein each term is derived from the previous term by multiplying by the common ratio -3. The first term a is -3, the common ratio r is -3 and there are 6 terms in the series, n = 6.
In order to calculate the sum of a geometric series, we use the formula S = a * (1 - r^n) / (1 - r).
Substituting the above values in the formula, we will get S = -3 * (1 - (-3) ^6) / (1 - (-3))
If we simplify this expression, we will get S = 546.
Therefore, the partial sum of the geometric series -3+9+-27...+729 equals 546.