Find the sum of the first 6 terms of the following sequence. Round to the nearest hundredth if necessary. 72,quad68.4,quad64.98,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 6 terms of the following sequence. Round to the nearest hundredth if necessary.  72,quad68.4,quad64.98,dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

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Find Common Ratio: First, we need to identify the common ratio (r) of the geometric sequence. We can find the common ratio by dividing the second term by the first term. Calculation: r = 68.4 / 72Calculate Common Ratio: Now, let's perform the calculation to find the common ratio. Calculation: r = 68.4 / 72 = 0.95Use Geometric Series Formula: Next, we will use the formula for the sum of the first n terms of a geometric series, which is S_n = (a_1 - a_1 * r^n) / (1 - r), where a_1 is the first term, r is the common ratio, and n is the number of terms. We have a_1 = 72, r = 0.95, and n = 6.Substitute Values and Calculate: Now, we will substitute the values into the formula and calculate the sum of the first 6 terms. Calculation: S_6 = (72 - 72 * 0.95^6) / (1 - 0.95)Perform Calculation for Sum: Let's perform the calculation for the sum. Calculation: S_6 = (72 - 72 * 0.95^6) / (1 - 0.95) = (72 - 72 * 0.7350918906249995) / 0.05Calculate Exact Sum: Now, we will calculate the exact value of the sum. Calculation: S_6 = (72 - 52.92660998379997) / 0.05 = 19.07339001620003 / 0.05 = 381.4678003240006Round to Nearest Hundredth: Finally, we will round the sum to the nearest hundredth as instructed. Calculation: S_6 ≈ 381.47

Find the sum of the first $6$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $72, \quad 68.4, \quad 64.98, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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