Find the sum of the first 6 terms of the following sequence. Round to the nearest hundredth if necessary. \[ 7, \quad-21, \quad 63, \ldots \] Sum of a finite geometric series: \[ S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r} \]

To find the sum of the first six terms of the sequence, we first identify that the sequence is geometric. The first term \( a_1 \) is 7, and the common ratio \( r \) can be found by dividing the second term by the first term: \( r = \frac{-21}{7} = -3 \). Now, we can use the formula for the sum of a finite geometric series: \[ S_{6} = \frac{a_{1}(1 - r^{n})}{1 - r} \] Plugging in the values: \[ S_{6} = \frac{7(1 - (-3)^{6})}{1 - (-3)} = \frac{7(1 - 729)}{1 + 3} = \frac{7(-728)}{4} = \frac{-5096}{4} = -1274 \] Therefore, the sum of the first 6 terms of the sequence is \(-1274\).