Find the sum of the infinite geometric series. -4 - 2 - 1 - 1/2 + Write your answer as an integer or a fraction in simplest form. ______

Identify terms and ratio: Identify the first term (a_1) and the common ratio (r) of the geometric series. The first term a_1 is -4. To find the common ratio r, we divide the second term by the first term: r = a_2/a_1 = (-2)/(-4) = 1/2Use sum formula: Use the formula for the sum of an infinite geometric series, which is S = a_1/(1 - r), where S is the sum, a_1 is the first term, and r is the common ratio. We have a_1 = -4 and r = 1/2. Now, calculate the sum: S = (-4)/(1 - (1/2))Simplify and find sum: Simplify the expression to find the sum. S = (-4)/(1/2) S = -4 * (2/1) S = -8

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Find the sum of the infinite geometric series. $\newline$ $-4 - 2 - 1 - \frac{1}{2} +$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ $\_\_$

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Algebra 2

Find the value of an infinite geometric series

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Q. Find the sum of the infinite geometric series.

\newline

-4 - 2 - 1 - \frac{1}{2} +

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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 $a_1$ and the common ratio $r$ of the geometric series. $\newline$ The first term $a_1$ is $-4$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term: $\newline$ $r = \frac{a_2}{a_1} = \frac{-2}{-4} = \frac{1}{2}$
Use sum formula: Use the formula for the sum of an infinite geometric series, which is $S = \frac{a_1}{1 - r}$ , where $S$ is the sum, $a_1$ is the first term, and $r$ is the common ratio. $\newline$ We have $a_1 = -4$ and $r = \frac{1}{2}$ . $\newline$ Now, calculate the sum: $\newline$ $S = \frac{-4}{1 - (\frac{1}{2})}$
Simplify and find sum: Simplify the expression to find the sum. $\newline$ $S = \frac{-4}{\frac{1}{2}}$ $\newline$ $S = -4 \times \frac{2}{1}$ $\newline$ $S = -8$