Find the sum of the infinite geometric series. -3 - 6/5 - 12/25 - 24/125 + Write your answer as an integer or a fraction in simplest form. ______

Identify terms and ratio: Identify the first term (a) and the common ratio (r) of the geometric series. The first term a is -3. The common ratio r can be found by dividing the second term by the first term: r = (-6/5) / (-3) = 2/5.Check convergence: Determine if the series is convergent. A geometric series converges if the absolute value of the common ratio |r| is less than 1. In this case, |2/5| = 0.4, which is less than 1, so the series is convergent.Use sum formula: Use the formula for the sum of an infinite geometric series. The sum S of an infinite geometric series is given by S = a / (1 - r), where a is the first term and r is the common ratio.Calculate sum: Calculate the sum using the values of a and r. S = (-3) / (1 - (2/5)) S = (-3) / (5/5 - 2/5) S = (-3) / (3/5) S = (-3) * (5/3) S = -5

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Find the sum of the infinite geometric series. $\newline$ $-3 - \frac{6}{5} - \frac{12}{25} - \frac{24}{125} +$ $\newline$ 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.

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-3 - \frac{6}{5} - \frac{12}{25} - \frac{24}{125} +

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

\newline

______

Identify terms and ratio: Identify the first term $a$ and the common ratio $r$ of the geometric series. $\newline$ The first term $a$ is $-3$ . $\newline$ The common ratio $r$ can be found by dividing the second term by the first term: $r = (-6/5) / (-3) = 2/5$ .
Check convergence: Determine if the series is convergent. $\newline$ A geometric series converges if the absolute value of the common ratio $\lvert r \rvert$ is less than $1$ . $\newline$ In this case, $\lvert \frac{2}{5} \rvert = 0.4$ , which is less than $1$ , so the series is convergent.
Use sum formula: Use the formula for the sum of an infinite geometric series. $\newline$ The sum $S$ of an infinite geometric series is given by $S = \frac{a}{1 - r}$ , where $a$ is the first term and $r$ is the common ratio.
Calculate sum: Calculate the sum using the values of $a$ and $r$ . $S = \frac{-3}{1 - \left(\frac{2}{5}\right)}$ $S = \frac{-3}{\frac{5}{5} - \frac{2}{5}}$ $S = \frac{-3}{\frac{3}{5}}$ $S = (-3) \cdot \left(\frac{5}{3}\right)$ $S = -5$