Find the sum of the infinite geometric series. -4 - 12/5 - 36/25 - 108/125 + Write your answer as an integer or a fraction in simplest form. ______

Identify Terms and Ratio: To find the sum of an infinite geometric series, we need to identify the first term (a) and the common ratio (r) of the series. The formula for the sum of an infinite geometric series is S = a / (1 - r), where |r| < 1. The first term of the series is -4, and by comparing the first two terms, we can find the common ratio by dividing the second term by the first term: r = (-12/5) / (-4) = 3/5.Apply Formula: Now that we have the first term (a = -4) and the common ratio (r = 3/5), we can use the formula for the sum of an infinite geometric series: S = a / (1 - r). Let's plug in the values: S = -4 / (1 - 3/5).Plug in Values: We need to simplify the expression: S = -4 / (1 - 3/5) = -4 / (2/5) = -4 * (5/2) = -20/2.Simplify Expression: Simplifying the fraction -20/2 gives us -10. So, the sum of the infinite geometric series is -10.

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Find the sum of the infinite geometric series. $\newline$ $-4 - \frac{12}{5} - \frac{36}{25} - \frac{108}{125} +$ $\newline$ 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

-4 - \frac{12}{5} - \frac{36}{25} - \frac{108}{125} +

\newline

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

\newline

______

Identify Terms and Ratio: To find the sum of an infinite geometric series, we need to identify the first term $a$ and the common ratio $r$ of the series. The formula for the sum of an infinite geometric series is $S = \frac{a}{1 - r}$ , where |r| < 1. The first term of the series is $-4$ , and by comparing the first two terms, we can find the common ratio by dividing the second term by the first term: $r = \frac{-12/5}{-4} = \frac{3}{5}$ .
Apply Formula: Now that we have the first term $a = -4$ and the common ratio $r = \frac{3}{5}$ , we can use the formula for the sum of an infinite geometric series: $S = \frac{a}{1 - r}$ . $\newline$ Let's plug in the values: $S = \frac{-4}{1 - \frac{3}{5}}$ .
Plug in Values: We need to simplify the expression: $S = -\frac{4}{1 - \frac{3}{5}} = -\frac{4}{\frac{2}{5}} = -4 \times \frac{5}{2} = -\frac{20}{2}$ .
Simplify Expression: Simplifying the fraction $-\frac{20}{2}$ gives us $-10$ . So, the sum of the infinite geometric series is $-10$ .