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The series identified is a geometric progression with common ratio of half.
Formula for geometric progression:
Nth term of series = ar^(n-1), where a = first term value, r = common ratio
a) 7th term of the series = 64(1/2)^(7-1) = 64(1/2)^6
The ball reached a height of 1m after the 7th bounce
b) 9th term of series = 64(1/2)^8
The ball reached a height of 0.25m (25cm) after the 9th bounce.