Question

*20 pts*

You drop a ball from a height of 1.5 meters.
Each curved path has 74% of the height of the previous path.

a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.

b. What height will the ball be at the top of the sixth path?

Answer 1

A(n) = 150 x (0.74) n-1 ; 33.29 cm

Explanation:

1.5 meters turns into 150. & 74% turns to 0.74.

150 x (0.74) 6 -1 =

150 x (0.74) 5 = 33.285....

= round to 33.29

Answer 2

a. This is the geometric sequence: a1 = 1.5 m = 150 cm, r = 0.74

The formula now is an = a1 x r ^ n-1

Just substitute a1 = 150 cm and r = 0.74

an = 150 x (0.74) ^ n – 1

b. The second part is:

A6 = 150 x 0.74 ^ 6-1

= 150 x 0.74 ^5

= 150 x 0.221906624

= 33.28509936 cm