Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 12,quad-18,quad27,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.  12,quad-18,quad27,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 sequence, we first need to identify the type of sequence we are dealing with. By observing the pattern, we can see that each term is multiplied by -1.5 to get the next term. This indicates that the sequence is a geometric sequence with a common ratio (r) of -1.5. The first term (a_1) is 12.Calculate Common Ratio: Using the formula for the sum of the first n terms of a geometric series, S_n = (a_1 - a_1 * r^n) / (1 - r), we can calculate the sum of the first 8 terms. Here, a_1 = 12, r = -1.5, and n = 8.Apply Geometric Series Formula: Plugging the values into the formula, we get S_8 = (12 - 12 * (-1.5)^8) / (1 - (-1.5)).Calculate (-1.5)^8: Calculating the value of (-1.5)^8, we get (-1.5)^8 = 256.2890625.Substitute Values into Formula: Now, we substitute this value into the formula: S_8 = (12 - 12 * 256.2890625) / (1 + 1.5).Perform Multiplication and Subtraction: Performing the multiplication and subtraction, we get S_8 = (12 - 3075.46875) / 2.5.Calculate Numerator: Calculating the numerator, we get 12 - 3075.46875 = -3063.46875.Divide by 2.5: Finally, we divide by 2.5 to find the sum: S_8 = -3063.46875 / 2.5.Final Sum Calculation: Performing the division, we get S_8 = -1225.3875.Round to Nearest Hundredth: Rounding to the nearest hundredth, the sum of the first 8 terms is approximately -1225.39.

Find the sum of the first $8$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $12, \quad-18, \quad 27, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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