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Find the sum of the infinite geometric series.\newline−7−72−74−78+-7 - \frac{7}{2} - \frac{7}{4} - \frac{7}{8} + \newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_

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Q. Find the sum of the infinite geometric series.\newline−7−72−74−78+-7 - \frac{7}{2} - \frac{7}{4} - \frac{7}{8} + \newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_
  1. Identify first term and ratio: Identify the first term (a1a_1) and the common ratio (rr) of the geometric series.\newlinea1=−7a_1 = -7 (the first term)\newlineTo find the common ratio, divide the second term by the first term:\newliner=second termfirst term=−7/2−7=12r = \frac{\text{second term}}{\text{first term}} = \frac{-7/2}{-7} = \frac{1}{2}
  2. Apply sum formula: Apply the formula for the sum of an infinite geometric series, which is S=a11−rS = \frac{a_1}{1 - r}, where SS is the sum, a1a_1 is the first term, and rr is the common ratio.\newlineHere, a1=−7a_1 = -7 and r=12r = \frac{1}{2}.\newlineCalculate the sum:\newlineS=−71−12S = \frac{-7}{1 - \frac{1}{2}}
  3. Simplify denominator and solve: Simplify the denominator and solve for SS:S=−7(12)S = -\frac{7}{\left(\frac{1}{2}\right)}S=−7×(21)S = -7 \times \left(\frac{2}{1}\right)S=−14S = -14

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