Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 36,quad9,quad(9)/(4),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.  36,quad9,quad(9)/(4),dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

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Identify Sequence Type: To find the sum of the first 9 terms of the given sequence, we first need to identify the type of sequence. The sequence provided is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. To find this common ratio (r), we divide the second term by the first term.Calculate Common Ratio: Calculate the common ratio (r): r = 9 / 36 r = 1 / 4Use Geometric Series Formula: Now that we have the common ratio, we can 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) where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.Find Sum of First 9 Terms: Plug the values into the formula to find the sum of the first 9 terms: S_9 = (36 - 36 * (1/4)^9) / (1 - 1/4)Calculate Numerator and Denominator: Calculate the numerator and the denominator separately: Numerator: 36 - 36 * (1/4)^9 Denominator: 1 - 1/4Calculate Denominator: Calculate the denominator: Denominator = 1 - 1/4 = 3/4Calculate Numerator: Calculate the numerator: Numerator = 36 - 36 * (1/4)^9 Since (1/4)^9 is a very small number, we can use a calculator to find its value and then multiply it by 36.Divide Numerator by Denominator: Using a calculator, we find: (1/4)^9 ≈ 0.0000152587890625 Numerator = 36 - 36 * 0.0000152587890625 ≈ 36 - 0.0005488125 Numerator ≈ 35.9994511875Calculate Final Sum: Now, divide the numerator by the denominator to find the sum: S_9 = 35.9994511875 / (3/4) S_9 = 35.9994511875 * (4/3)Round to Nearest Hundredth: Calculate the final sum: S_9 ≈ 35.9994511875 * (4/3) S_9 ≈ 47.99926825Round the sum to the nearest hundredth: S_9 ≈ 48.00

Find the sum of the first $9$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $36, \quad 9, \quad \frac{9}{4}, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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