Find the sum of the infinite geometric series. -10 - 5/2 - 5/8 - 5/32 + Write your answer as an integer or a fraction in simplest form. ______

Identify Terms: First, we need to identify the first term (a) and the common ratio (r) of the geometric series. The first term a is -10. To find the common ratio r, we divide the second term by the first term: r = (-5/2) / (-10) = 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 Sum Formula: Let's plug the values into the formula: S = -10 / (1 - 1/4) S = -10 / (3/4) S = -10 * (4/3)Plug in Values: Now, we perform the multiplication to find the sum: S = -40/3 This is the sum of the infinite geometric series in fraction form.

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Find the sum of the infinite geometric series. $\newline$ $-10 - \frac{5}{2} - \frac{5}{8} - \frac{5}{32} +$ $\newline$ 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

-10 - \frac{5}{2} - \frac{5}{8} - \frac{5}{32} +

\newline

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

\newline

______

Identify Terms: First, we need to identify the first term $a$ and the common ratio $r$ of the geometric series. $\newline$ The first term $a$ is $-10$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term: $r = \frac{-5/2}{-10} = \frac{1}{4}$ .
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 Sum Formula: Let's plug the values into the formula: $\newline$ $S = \frac{-10}{1 - \frac{1}{4}}$ $\newline$ $S = \frac{-10}{\frac{3}{4}}$ $\newline$ $S = -10 \times \frac{4}{3}$
Plug in Values: Now, we perform the multiplication to find the sum: $\newline$ $S = -\frac{40}{3}$ $\newline$ This is the sum of the infinite geometric series in fraction form.