A ball is dropped from a height of 3 m. After each bounce it rises to 75% of its previous height.

a) State t1 and r:t1 = 3 m r = 0.75

b) Write the general term for the sequence:

tn = (t1)(r^n-1)

tn = (3)(0.75^n-1)

c) What height does the ball reach after the 6th bounce?(I am not sure how to do this question)

This was my attempt: I suppose you solve for tn and you plug in 6 into n...

tn = (3)(0.75^6-1)

tn = (3)(0.75^5)

tn = (3)(.2373046875)

tn = .7119140625

My answer was wrong, the answer is53.39 cm.

(I cannot solve this one either)

d) After how many bounces will the ball reach a height of approx. 40 cm?

My attempt: I plugged in 40 cm into tn and try to solve for n:

40 = (3)(0.75^n-1)

13.3 = 0.75^n-1I am stuck here... I do not know how to get n alone with algebra....

The answer is 7 times.

Could anyone tell me where I went wrong for c) and d) and what I should have done? Thanks!