A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
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Answers
Answer:
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Step-by-step explanation:
The height reached by the bouncing ball forms a geometric progression
27, 18, 12
Common ratio = 18/27 = 12/18 = 2/3
The nth term is given by = ar^(n-1)
Where a = first term = 27
r = common ratio = 2/3
The fourth peak = 4th term = 27x(2/3)^3
= 8 feet
f(1) = 6 and n ≥ 1? 6, 1, –4, –9, –14,…
The above values form an arithmetic progression with:
First term, a = 6
Common difference, d = -5
Nth term = a + (n-1)d
= 6 + (n-1)-5
= 6 - 5n + 5
= 11 – 5n
Answer:
Step-by-step explanation:
Sample response:
There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.