Find the sum of the first 6 terms of the following sequence. Round to the nearest hundredth if necessary.
\( 100, \quad 87, \quad 75.69, \ldots \)
Sum of a finite geometric series:
\[
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
\]
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Step 3: Calculate the sum of the first 6 terms: \(S_6\) = \(\frac{100(1-0.87^6)}{1-0.87} \approx 420.21\)

Steps

Step 1 ：Step 1: Find the common ratio\(r\) by dividing the second term by the first term: \(r = \frac{87}{100} = 0.87\)

Step 2 ：Step 2: Use the formula for the sum of the first n terms of a geometric series: \(S_n = \frac{a_1(1-r^n)}{1-r}\)

Step 3 ：Step 3: Calculate the sum of the first 6 terms: \(S_6\) = \(\frac{100(1-0.87^6)}{1-0.87} \approx 420.21\)