The height a ball bounces is less than the height of the previous bounce due to friction. The heights of the bounces form a geometric sequence. Suppose a ball is dropped from one meter and rebounds 95 % of the height of the previous bounce. What is the total distance traveled by the ball when it comes to rest? Does the problem give you enough information to solve the problem? How can you write the general term of the sequence? What formula should you use to calculate the total distance?

Let the first height be h. second height. 75h

third height. 75h. fourth height. 75²h

fifth height. 75²h, sixthth height. 75³ and so on

Total distance consists of two geometric series as follows

1) first series

h +.75h +.75²h +.75³h ...

2) second series

.75h +.75²h +.75³h +.75⁴h ...

Sum of first series:

first term a = h, commom ratio r =.75

sum = a / (1 - r)

= h / 1 -.75

= h /.25

4h

sum of second series : --

first term a =.75 h, commom ratio r =.75

sum = a / (1 - r)

=.75h / 1 -.75

=.75h /.25

3h

Total of both the series

= 4h + 3h

= 7h.

h = 1 m

Total distance = 7 m