To solve this problem, we need to determine the common ratio in the geometric sequence. We can do this by examining the ratios between the heights of consecutive bounces.
The ratio between the second bounce and the first bounce is 320/400 = 0.8.
The ratio between the third bounce and the second bounce is 256/320 = 0.8.
Therefore, the common ratio is 0.8.
To find the height of the ball on the 8th bounce, we can multiply the height of the ball on the first bounce by the common ratio raised to the power of 7 (since we are counting the first bounce as the 1st bounce, not the 0th bounce).
Height of 8th bounce = 400 * (0.8)^7
Height of 8th bounce ≈ 400 * 0.2097152 ≈ 83.89 meters
Rounding to the nearest meter, the ball bounces approximately 84 meters on the 8th bounce.
A ball is dropped from a height of 500 meters. The table below shows the ball bounced 400 meters on the first bounce, 320 meters on the second bounce, and 256 meters on the third bounce. the heights form a geometric sequence. How high does the ball bounce on the 8th bounce? Round your answer to the nearest meter.
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