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: Submit Amswer attempt 2 out of 2
Solution
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 ：\( S_{7} = 3650 \)
