I NEED HELP PLEASE, THANKS! :) Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second. (Show work)

Hey there! :)

f(15) = 29 ft.

Step-by-step explanation:

We can write an arithmatic equation for this pattern:

Where:

= 1, = 3

Find the rate of change. This is constant because this is an arithmatic sequence.

3 - 1 = 2.

We can begin to write an explicit function for this situation:

f(n) = + d(n-1) where d is the rate of change:

f(n) = 1 + 2(n-1)

Substitute 15 for n to solve for the distance traveled after 15 seconds:

f(15) = 1 + 2(15-1)

f(15) = 1 + 2(14)

f(15) = 1 + 28

f(15) = 29 ft.

Therefore, the distance traveled after 15 seconds is 29 ft.