Find the sum of the infinite geometric series. -10 - 15/2 - 45/8 - 135/32 + 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 = (-15/2) / (-10) = 3/4Calculate 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, |3/4| < 1, so we can use the formula.Use Sum Formula: Let's calculate the sum using the formula: S = a / (1 - r) = -10 / (1 - 3/4)Simplify Denominator: Simplify the denominator: 1 - 3/4 = 1/4Divide First Term: Now, divide the first term by the simplified denominator: S = -10 / (1/4) = -10 * (4/1) = -40

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Find the sum of the infinite geometric series. $\newline$ $-10 - \frac{15}{2} - \frac{45}{8} - \frac{135}{32} +$ $\newline$ 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{15}{2} - \frac{45}{8} - \frac{135}{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. $\newline$ $r = \frac{-15/2}{-10} = \frac{3}{4}$
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{3}{4}| < 1, so we can use the formula.
Use Sum Formula: Let's calculate the sum using the formula: $\newline$ $S = \frac{a}{1 - r} = \frac{-10}{1 - \frac{3}{4}}$
Simplify Denominator: Simplify the denominator: $1 - \frac{3}{4} = \frac{1}{4}$
Divide First Term: Now, divide the first term by the simplified denominator: $\newline$ $S = -\frac{10}{\left(\frac{1}{4}\right)} = -10 \times \left(\frac{4}{1}\right) = -40$