Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100 cm and a return swing of 99 cm.

a.)On which swing will the length first have a length less than 50 cm?

b.)Find the total distance traveled by the pendulum until it comes to rest.

Question

Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100 cm and a return swing of 99 cm. 

a.)On which swing will the length first have a length less than 50 cm? 

b.)Find the total distance traveled by the pendulum until it comes to rest.