hard question for me

Question

10.You drop a ball from a height of 1.5 meters. Each curved path has 75% 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) The sequence can be written down as follows:

1.5 X 100 (converting to cm) , 1.5 X 100 X 0.75, 1.5 X 100 X 0.75², 1.5 X 100 X 0.75³..................

Thus, nth term (height) = 1.5 X 100 X (0.75)^n-1

b) The height of the 6th path = 1.5 X 100 X (0.75)^6-1

= 1.5 X 100 X (0.75)⁵

= 35.6 cm