Digital ACT Math Practice Question #851
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Set up the infinite sum formula: \( S_\infty = \frac{a_1}{1 - r} \).
Divide: \( 1 - r = 18/54 = 1/3 \). Then subtract from 1 to solve for \( r \).
The sum of an infinite geometric series is given by \( S_\infty = \frac{a_1}{1 - r} \) for \( |r| < 1 \). Given \( a_1 = 18 \) and \( S_\infty = 54 \): \[ 54 = \frac{18}{1 - r} \implies 1 - r = \frac{18}{54} = \frac{1}{3} \] \[ r = 1 - \fra...
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