Find the sum of the infinite geometric series. -7 - 7/2 - 7/4 - 7/8 + Write your answer as an integer or a fraction in simplest form. ______

Identify first term and ratio: Identify the first term (a_1) and the common ratio (r) of the geometric series. a_1 = -7 (the first term) To find the common ratio, divide the second term by the first term: r = (second term) / (first term) = (-7/2) / (-7) = 1/2Apply sum formula: Apply 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. Here, a_1 = -7 and r = 1/2. Calculate the sum: S = -7 / (1 - 1/2)Simplify denominator and solve: Simplify the denominator and solve for S: S = -7 / (1/2) S = -7 * (2/1) S = -14

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Find the sum of the infinite geometric series. $\newline$ $-7 - \frac{7}{2} - \frac{7}{4} - \frac{7}{8} +$ $\newline$ 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

-7 - \frac{7}{2} - \frac{7}{4} - \frac{7}{8} +

\newline

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

\newline

\_\_

Identify first term and ratio: Identify the first term ( $a_1$ ) and the common ratio ( $r$ ) of the geometric series. $\newline$ $a_1 = -7$ (the first term) $\newline$ To find the common ratio, divide the second term by the first term: $\newline$ $r = \frac{\text{second term}}{\text{first term}} = \frac{-7/2}{-7} = \frac{1}{2}$
Apply sum formula: Apply 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. $\newline$ Here, $a_1 = -7$ and $r = \frac{1}{2}$ . $\newline$ Calculate the sum: $\newline$ $S = \frac{-7}{1 - \frac{1}{2}}$
Simplify denominator and solve: Simplify the denominator and solve for $S$ : $S = -\frac{7}{\left(\frac{1}{2}\right)}$ $S = -7 \times \left(\frac{2}{1}\right)$ $S = -14$