Sun Of An Object Is Dropped From The Top Of A Building And Falls 16ft. In The 1st Second. It Falls Three Times As Far During The 2nd Second, Five Time

sun of an object is dropped from the top of a building and falls 16ft. in the 1st second. it falls three times as far during the 2nd second, five times as far during the 3rd second, and so on in arithmetic sequence. how far will it have fallen in 10 seconds?

 

Answer:

The object will have fallen 304 feet in 10 seconds.

Step-by-step explanation:

The time in seconds is the term or nth term, n.

The distance in feet is the corresponding sequence.

To find the arithmetic sequence:

a₁ = 16 ft

a₂ = 16×3 = 48 ft (3 times as far as the distance on the first second.)

a₃ = 16×5 = 80 ft (5 times as far as the distance on the first second.)

To solve for the common difference (d):

a₂-a₁ = a₃-a₂

48-16 = 80-48

32 = 32

The arithmetic sequence:  16, 48, 80

The common difference (d): 32

Arithmetic sequence general rule:

an = a₁ + (n-a)(d)

Where:

an = last term

n = the term o nth position in the sequence

a₁ = the first term

d = common difference

Find the distance on the 10th second, n=10:

a₁₀ = 16 + (10-1)(32)

a₁₀ = 16 + (9)(32)

a₁₀ = 16 + 288

a₁₀ = 304