Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary. 28,quad35,quad43.75,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.  28,quad35,quad43.75,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: First, we need to identify the type of sequence we are dealing with. By looking at the given terms, we can see that each term is obtained by multiplying the previous term by a constant ratio. This indicates that the sequence is a geometric series.Find terms and ratio: To find the sum of the first 10 terms of a geometric series, we need to identify the first term (a_1), the common ratio (r), and the number of terms (n). The first term a_1 is given as 28. To find the common ratio, we divide the second term by the first term: r = 35 / 28 = 1.25.Calculate sum formula: Now that we have the first term a_1 = 28 and the common ratio r = 1.25, we can use the formula for the sum of the first n terms of a geometric series: S_n = (a_1(1 - r^n)) / (1 - r). We will use n = 10 since we want to find the sum of the first 10 terms.Substitute values: Plugging the values into the formula, we get S_10 = (28(1 - 1.25^10)) / (1 - 1.25). Now we need to calculate 1.25^10 and then proceed with the rest of the calculation.Calculate 1.25^10: Calculating 1.25^10 gives us approximately 9.31322575. Now we can substitute this value into the formula: S_10 = (28(1 - 9.31322575)) / (1 - 1.25).Simplify expression: Simplifying the expression, we get S_10 = (28(-8.31322575)) / (-0.25). This simplifies to S_10 = -28 * 8.31322575 / -0.25.Final sum calculation: Performing the multiplication and division, we find S_10 = 231.970318 / -0.25, which equals -927.881272. Since we are summing a series of positive terms, getting a negative sum indicates a mistake in the calculation.

Find the sum of the first $10$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $28, \quad 35, \quad 43.75, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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