Solve the problem.
-A pendulum bob swings through an arc 50 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?
A)83 inches
B)143 inches
C)167 inches
D)71 inches

Question

Quizplus · Accepted Answer

This problem describes a geometric series where the first term $a = 50$ inches and the common ratio $r = 0.7$. The sum $S$ of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Substituting the given values, $S = \frac{50}{1 - 0.7} = \frac{50}{0.3} = 166.67$ inches, which rounds to 167 inches, making option C correct.

Solve the Problem. -A Pendulum Bob Swings Through an Arc 50 Inches Long