A pendulum travels 3 feet on its first swing, and each later swing covers three-quarters of the distance of the swing before it. What total distance does the pendulum travel before it comes to rest?

1. The swing lengths form an infinite geometric series with first term a_1 = 3 feet and ratio r = 3/4. 2. Because the ratio sits strictly between -1 and 1, the infinite sum is defined. 3. Apply the formula S = a_1/(1 - r). 4. The denominator is 1 - 3/4 = 1/4. 5. S = 3 / (1/4) = 3 x 4 = 12 feet of total travel. 6. Option A, 9 feet, multiplies 3 by the ratio sum 3/4 x 4 and misplaces the first term. 7. Option B, 4 feet, inverts the calculation by dividing the denominator into 1 instead of into 3. 8. Option C, 16 feet, uses a first term of 4 feet, which the problem never states. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 SERIES AND THEIR NOTATIONS_