Problem
29. Given the geometric series \( 300+360+432+518.4+\ldots \), write a geometric series formula, \( S_{n} \), for the sum of the first \( n \) terms. Use the formula to find the sum of the first 10 terms, to the nearest tenth.
Solution
Step 1 ：Identify: a = 300, r = \( \frac{360}{300} = \frac{6}{5} \), n = 10
Step 2 ：Formula: \( S_{n} = \frac{a(r^{n}-1)}{r-1} \)
Step 3 ：Calculate: \( S_{10} = \frac{300((\frac{6}{5})^{10}-1)}{\frac{6}{5}-1} \approx 16218.3 \)
