Find the sum of the infinite geometric series. –10 – 5 – 5/2 – 5/4 + ⋯ Write your answer as an integer or a fraction in simplest form. ______

Identify the first term: Identify the first term (a_1) of the geometric series. The first term a_1 is the first number in the series, which is -10.Determine the common ratio: Determine the common ratio (r) of the geometric series. The common ratio r can be found by dividing the second term by the first term: r = a_2/a_1 = (-5)/(-10) = 1/2.Use the formula for the sum: Use the formula for the sum of an infinite geometric series. The formula is S = a_1/(1 - r), where S is the sum, a_1 is the first term, and r is the common ratio.Plug the values into the formula: Plug the values of a_1 and r into the formula to find the sum. S = (-10)/(1 - (1/2)) = (-10)/(1/2) = (-10) * (2/1) = -20.

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Find the sum of the infinite geometric series. $\newline$ $-10 - 5 - \frac{5}{2} - \frac{5}{4} + \cdots$ $\newline$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ $\underline{\hspace{3em}}$ $\newline$

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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.

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-10 - 5 - \frac{5}{2} - \frac{5}{4} + \cdots

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

\newline

\underline{\hspace{3em}}

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Identify the first term: Identify the first term $a_1$ of the geometric series. $\newline$ The first term $a_1$ is the first number in the series, which is $-10$ .
Determine the common ratio: Determine the common ratio $r$ of the geometric series. $\newline$ The common ratio $r$ can be found by dividing the second term by the first term: $r = \frac{a_2}{a_1} = \frac{-5}{-10} = \frac{1}{2}$ .
Use the formula for the sum: Use the formula for the sum of an infinite geometric series. $\newline$ The formula is $S = \frac{a_1}{1 - r}$ , where $S$ is the sum, $a_1$ is the first term, and $r$ is the common ratio.
Plug the values into the formula: Plug the values of $a_1$ and $r$ into the formula to find the sum. $\newline$ $S = \frac{-10}{1 - (\frac{1}{2})} = \frac{-10}{\frac{1}{2}} = (-10) \cdot \frac{2}{1} = -20$ .