Question

A pendulum swings in an arc in which each successive swing is 40% as long as the previous swing. if the first swing covers an arc 75 meters long, what is the total distance the pendulum will swing before coming to rest? 250 meters 125 meters 100 meters 190 meters

Answer 1

The situation given above is that of the geometric sequence with first term equal to 75 meters and the common ratio equal to 0.40. The sum of the terms for an infinite geometric sequence is expressed in the equation,
                                 S = a1/(1 - r)
Substituting,
                               S = (75 m) / (1 - 0.4) = 125 m
Therefore, the total distance that the pendulum had swung before finally coming to rest is 125 m.