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of 900 centimeters. The table shows the height of each bounce.

Bounce Height (cm)
1 800
2 560
3 392

The heights form a geometric sequence.

How high does the ball bounce on the 5th bounce? Round your answer to the nearest tenth of a centimeter, if necessary.

Respuesta :

Edufirst

Answer:

  • Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.

Explanation:

The ball is dropped from a height of 900 centimeters.

Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:

  • Height bounce 2 / height bounce 1 = 560 / 800 = 0.7
  • Height bound 3 / height bounce 2 = 392 / 560 = 0.7

Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:

            [tex]a_n=800(0.7)^{n-1}[/tex]

With that formula you can find any term:

             [tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]

Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.

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