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)

Answer

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Answer

So, the sum of the first 6 terms of the geometric series is $\boxed{-441}$

Steps

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 $\boxed{-441}$