14. A basketball tossed vertically upwards reaches a maximum height and then falls to the floor. Assume that we have an “ideal" basketball which rebounds to exactly 0.8 of its previous height. Let a, be the height after the n-th bounce, with the initial height being 4 metres. (a) Find both a recursive definition and an explicit formula for the sequence {an}. (Hint: Start by writing out the first four or five terms of the sequence.) (b) What is the height after the 10th bounce? (You may use a calculator!) (c) Make a conjecture about the limit of the sequence.

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A:

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