Find the sum of the infinite geometric series. -6 - 3/2 - 3/8 - 3/32 + Write your answer as an integer or a fraction in simplest form. ______

Identify first term and common ratio: First, we need to identify the first term (a) and the common ratio (r) of the geometric series. The first term a is -6. To find the common ratio r, we divide the second term by the first term: r = (-3/2) / (-6) = 1/4.Calculate common ratio: Now that we have the first term and the common ratio, we can use the formula for the sum of an infinite geometric series, which is S = a / (1 - r), provided that |r| < 1. In this case, |1/4| < 1, so we can use the formula.Use formula for sum: Let's plug the values into the formula: S = (-6) / (1 - 1/4).Plug values into formula: Now we calculate the denominator: 1 - 1/4 = 4/4 - 1/4 = 3/4.Calculate denominator: Next, we calculate the sum: S = (-6) / (3/4). To divide by a fraction, we multiply by its reciprocal: S = (-6) * (4/3).Calculate sum: Now we perform the multiplication: S = -24/3.Simplify fraction: Finally, we simplify the fraction: S = -8.

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Find the sum of the infinite geometric series. $\newline$ $-6 - \frac{3}{2} - \frac{3}{8} - \frac{3}{32} +$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ ______

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Precalculus

Find the value of an infinite geometric series

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Q. Find the sum of the infinite geometric series.

\newline

-6 - \frac{3}{2} - \frac{3}{8} - \frac{3}{32} +

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

______

Identify first term and common ratio: First, we need to identify the first term $a$ and the common ratio $r$ of the geometric series. $\newline$ The first term $a$ is $-6$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term: $r = \frac{-3/2}{-6} = \frac{1}{4}$ .
Calculate common ratio: Now that we have the first term and the common ratio, we can use the formula for the sum of an infinite geometric series, which is $S = \frac{a}{(1 - r)}$ , provided that |r| < 1. In this case, |\frac{1}{4}| < 1, so we can use the formula.
Use formula for sum: Let's plug the values into the formula: $S = \frac{-6}{1 - \frac{1}{4}}$ .
Plug values into formula: Now we calculate the denominator: $1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}$ .
Calculate denominator: Next, we calculate the sum: $S = (-6) / (\frac{3}{4})$ . To divide by a fraction, we multiply by its reciprocal: $S = (-6) \times (\frac{4}{3})$ .
Calculate sum: Now we perform the multiplication: $S = \frac{-24}{3}$ .
Simplify fraction: Finally, we simplify the fraction: $S = -8$ .