Using a geometric sequence, it is found that:
- The rule for the height of the nth bounce is:

- The height of the fifth bounce is of 9.28 cm.
In a <em>geometric sequence</em>, the quotient between consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:

In which
is the first term.
In this problem:
- Bounces to 65% of the height from which it was dropped, thus the common ratio is of
. - Dropped from 80 cm, thus, the height of the first bounce is
.
Thus, the rule for the height of the nth bounce is:

The height of the fifth bounce is
, thus:

The height of the fifth bounce is of 9.28 cm.
A similar problem is given at brainly.com/question/11847927