An object in free fall is dropped from a tall cliff. It falls 16 ft in the first second, 48 ft in the second second, 80 ft in the third second, and so on.a. Write a formula for the nth term of an arithmetic sequence that represents the distance dn (in ft) that the object will fall in the nth second.b. How far will the object fall in the 8th second?c.What is the total distance that the object will fall in 8 sec?

Question
Asked Dec 21, 2019
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An object in free fall is dropped from a tall cliff. It falls 16 ft in the first second, 48 ft in the second second, 80 ft in the third second, and so on.

a. Write a formula for the nth term of an arithmetic sequence that represents the distance dn (in ft) that the object will fall in the nth second.

b. How far will the object fall in the 8th second?

c.What is the total distance that the object will fall in 8 sec?

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Expert Answer

Step 1

Step 1:

The object fall in the first second = 16ft  

The object fall in the second second = 48ft

The object fall in the third second = 80ft

So, it become a arithmetic sequence with common difference 32.

The formula for the nth term of an arithmetic sequence is:

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а, —а+(п-1)d where a is the first term of the sequence d is the common difference in terms

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Step 2
  1. b) the above formula represent the distance that falls on every second after n seconds:
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a, = a+(n-1)d a̟ =16+(8–1)·32 =16+7(32) =16+ 224 = 240

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Step 3

The total distance that the obje...

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s, =(2a+(n-1)d) (2(16)+(8–1)(32)) =1024

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Algebra