Question

A ball is dropped from a height of 10 feet. The ball bounces to 90% of its previous height with each bounce. Identify the geometric sequence that shows the height of the fourth bounce in bold (to the nearest tenth). A) 8.1, 7.3, 6.6, 5.9,... B) 9, 8.1, 7.3, 6.6,... C) 9, 8, 7, 6,... D) 9, 8.1, 7.3, 5.6,...

Answer 1

The geometric sequence that shows the height of the fourth bounce in bold is B) 9, 8.1, 7.3, 6.6,...

Answer 2

Original height=10 feet
Height after first bounce: (10 feet)*90%=(10 feet)*90/100=9 feet
Height after second bounce: (9 feet)*90%=(9 feet)*90/100=8.1 feet
Height after third bounce: (8.1 feet)*90%=(8.1 feet)*90/100=7.29 feet = 7.3 feet
Height after fourth bounce: (7.29 feet)*90%=(7.29 feet)*90/100=6.561 feet=6.6 feet

Answer: Option B) 9, 8.1, 7.3, 6.6,...