b) the sum of the first 6 terms of the following geometric series: $7,14,28,56, \ldots$ \[ S_{6}=\text { Number I } \] (round your answer to the nearest integer if applicable)

Step 1 ：This 6-term geometric series has first term $a_0 = 7$ and ratio $2$, so it has value

Step 2 ：\begin{align*} \frac{7(1-(2)^{6})}{1-2} &= 7(1-64) \end{align*}

Step 3 ：\begin{align*} &= 7(-63) \end{align*}

Step 4 ：\begin{align*} &= -441 \end{align*}

Step 5 ：So, the sum of the first 6 terms of the geometric series is \(\boxed{-441}\)