Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 50,quad44,quad38.72,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 8 terms of the following sequence. Round to the nearest hundredth if necessary.  50,quad44,quad38.72,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 8 terms of the given sequence, we first need to identify the type of sequence. We can see that the sequence is decreasing, and each term is a fixed percentage of the previous term, which suggests that it is a geometric sequence. To confirm this, we need to find the common ratio (r) by dividing the second term by the first term.Calculate common ratio: Calculate the common ratio (r) by dividing the second term (44) by the first term (50). r = 44 / 50 r = 0.88Use sum 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.Plug values into formula: Plug the values into the formula to find the sum of the first 8 terms. a_1 = 50 (the first term) r = 0.88 (the common ratio) n = 8 (the number of terms) S_8 = (50 - 50 * 0.88^8) / (1 - 0.88)Calculate sum: Calculate the sum using the values provided. S_8 = (50 - 50 * 0.88^8) / (1 - 0.88) S_8 = (50 - 50 * 0.271) / 0.12 S_8 = (50 - 13.55) / 0.12 S_8 = 36.45 / 0.12 S_8 = 303.75Round sum: Round the sum to the nearest hundredth if necessary. In this case, the sum is already at the hundredth place, so no rounding is needed.

Find the sum of the first $8$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $50, \quad 44, \quad 38.72, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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