Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary. 12,quad2,quad(1)/(3),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.  12,quad2,quad(1)/(3),dots Sum of a finite geometric series:  S_(n)=(a_(1)-a_(1)r^(n))/(1-r) Answer:

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Identify terms and values: First, identify the first term (a_1), the common ratio (r), and the number of terms (n) in the sequence. The first term a_1 is 12. The second term is 2, so the common ratio r can be found by dividing the second term by the first term: r = 2 / 12 = 1/6. The number of terms n we want to find the sum of is 10.Calculate common ratio: Now, 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) Plug in the values we have: a_1 = 12, r = 1/6, and n = 10.Use formula for sum: Calculate the value of r^n (1/6)^10. This requires a calculator or a software tool to find the precise value.Calculate r^n: After calculating (1/6)^10, we find that it is a very small number (approximately 1.65381717e-08). For practical purposes, when subtracting this value from 12 in the numerator, it will have an insignificant effect, so we can approximate the numerator to be just 12.Approximate numerator: Now, calculate the denominator (1 - r) = (1 - 1/6) = 5/6.Calculate denominator: Finally, calculate the sum S_10 using the approximated numerator and the calculated denominator: S_10 ≈ (12 - 0) / (5/6) S_10 ≈ 12 / (5/6) S_10 ≈ 12 * (6/5) S_10 ≈ 14.4

Find the sum of the first $10$ terms of the following sequence. Round to the nearest hundredth if necessary. $\newline$ $12, \quad 2, \quad \frac{1}{3}, \ldots$ $\newline$ Sum of a finite geometric series: $\newline$ $S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}$ $\newline$ Answer:

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