Problem

Find the sum of the following series. Round to the nearest hundredth if necessary.
\[
2+6+18+\ldots+4374
\]
Sum of a finite geometric series:
\[
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
\]
Answer:
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attempt 2 out of 2

Answer

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Answer

\( S_{7} = 3650 \)

Steps

Step 1 ：\( r = \frac{6}{2} = 3 \)

Step 2 ：\( n = \log_{3}{\frac{4374}{2}} = 7 \)

Step 3 ：\( S_{7} = \frac{2(1-3^{7})}{1-3} \)

Step 4 ：\( S_{7} = 3650 \)

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