Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary. 25,quad19.5,quad15.21,dots Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

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Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary.  25,quad19.5,quad15.21,dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

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Identify terms and ratio: Identify the first term (a_1) and the common ratio (r) of the geometric sequence. The first term a_1 is 25. To find the common ratio r, we divide the second term by the first term. r = 19.5 / 25Calculate common ratio: Calculate the common ratio (r). r = 19.5 / 25 r = 0.78Use sum formula: Use the formula for the sum of the first n terms of a geometric series: S_n = (a_1 - a_1 * r^n) / (1 - r). We have a_1 = 25, r = 0.78, and n = 10.Substitute and calculate sum: Substitute the values into the formula and calculate the sum. S_10 = (25 - 25 * 0.78^10) / (1 - 0.78)Calculate numerator: Calculate the numerator of the formula. 25 * 0.78^10 = 25 * (0.1073741824) ≈ 2.68435456Subtract to get numerator: Subtract the result from 25 to get the final numerator. 25 - 2.68435456 ≈ 22.31564544Calculate denominator: Calculate the denominator of the formula. 1 - 0.78 = 0.22Divide to find sum: Divide the numerator by the denominator to get the sum of the first 10 terms. S_10 = 22.31564544 / 0.22Perform division: Perform the division to find the sum S_10. S_10 ≈ 101.43429745Round to nearest hundredth: Round the sum to the nearest hundredth. S_10 ≈ 101.43

Find the sum of the first $10$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $25, \quad 19.5, \quad 15.21, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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