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.

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Accepted Answer

Step:1 ：Identify: a = 300, r = ( frac{360}{300} = frac{6}{5} ), n = 10Step: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 )

Answer

Step: 1 ：Identify: a = 300, r = ( frac{360}{300} = frac{6}{5} ), n = 10Step: 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 )

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.

Answer

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