A ball is dropped from a height of and rebounds to of the height from which it falls…

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A ball is dropped from a height of

125\,\text{m}

and rebounds to

60\%

of the height from which it falls after each bounce. (i) Express the height reached after the

n

th bounce in the form of a sequence and state the common ratio. (ii) Calculate the height reached after the

6

th bounce. (iii) Determine the smallest integer

n

for which the height after the

n

th bounce is less than

5\,\text{m}

. Show all working steps.