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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