Find the sum of the first 7 terms of the following series, to the nearest integer. 6,9,(27)/(2),dots Answer:

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Find the sum of the first 7 terms of the following series, to the nearest integer.  6,9,(27)/(2),dots Answer:

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Identify Pattern: The given series is not an arithmetic or geometric series, but we can observe a pattern in the first three terms. The first term is 6, the second term is 9 which is 1.5 times the first term, and the third term is (27/2) which is 1.5 times the second term. This suggests that each term is 1.5 times the previous term, indicating that the series is a geometric series with the first term a = 6 and the common ratio r = 1.5.Apply Geometric Series Formula: To find the sum of the first 7 terms of a geometric series, we use the formula for the sum of the first n terms of a geometric series, which is Sn = a(1 - rn) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.Substitute Values: We will now apply the formula with a = 6, r = 1.5, and n = 7 to find the sum of the first 7 terms. S7 = 6(1 - 1.57) / (1 - 1.5)Calculate Exponent: Calculating the value of 1.57 and then substituting it into the formula. 1.57 ≈ 17.0859375 S7 = 6(1 - 17.0859375) / (1 - 1.5)Perform Subtraction: Now, we will perform the subtraction in the numerator and the denominator. S7 = 6(-16.0859375) / (-0.5)Calculate Sum: Finally, we will calculate the sum by performing the multiplication and division. S7 = -96.515625 / -0.5 S7 ≈ 193.03125Round to Nearest Integer: Since we need to find the sum to the nearest integer, we will round 193.03125 to the nearest integer. S7 ≈ 193

Find the sum of the first $7$ terms of the following series, to the nearest integer. $\newline$ $6,9, \frac{27}{2}, \ldots$ $\newline$ Answer:

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Find the sum of the first $7$ terms of the following series, to the nearest integer. $\newline$ $6,9, \frac{27}{2}, \ldots$ $\newline$ Answer: