Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 75,quad66,quad58.08,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 9 terms of the following sequence. Round to the nearest hundredth if necessary.  75,quad66,quad58.08,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 the first number in the sequence, which is 75. To find the common ratio r, we divide the second term by the first term. r = 66 / 75 = 0.88Use sum formula: Use the formula for the sum of the first n terms of a geometric series. We have a_1 = 75, r = 0.88, and n = 9. The formula for the sum of the first n terms (S_n) of a geometric series is: S_n = (a_1 - a_1 * r^n) / (1 - r)Substitute and calculate: Substitute the values into the formula and calculate the sum. S_9 = (75 - 75 * 0.88^9) / (1 - 0.88) Now we calculate the numerator and the denominator separately. Numerator: 75 - 75 * 0.88^9 Denominator: 1 - 0.88Calculate numerator: Calculate the numerator. 75 - 75 * 0.88^9 = 75 - 75 * (0.23357214690901212) ≈ 75 - 17.5179 ≈ 57.4821Calculate denominator: Calculate the denominator. 1 - 0.88 = 0.12Divide to find sum: Divide the numerator by the denominator to find the sum. S_9 = 57.4821 / 0.12 ≈ 479.0175Round the result: Round the result to the nearest hundredth if necessary. S_9 ≈ 479.02

Find the sum of the first $9$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $75, \quad 66, \quad 58.08, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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