Solve the problem.
-A pendulum swings through an arc 80 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? If necessary,
Round to the nearest inch.
A)267 in.
B)133 in.
C)229 in.
D)114 in.

Question

Quizplus · Accepted Answer

This is a geometric series problem where the first term $a = 80$ inches and the common ratio $r = 0.70$. The sum $S$ of an infinite geometric series is given by $S = \frac{a}{1 - r}$, so substituting the given values, $S = \frac{80}{1 - 0.70} = \frac{80}{0.30} = 266.67$ inches, which rounds to 267 inches.

Solve the Problem. -A Pendulum Swings Through an Arc 80 Inches Long on Inches