Question

Suppose a ball is thrown upward to a height of h 0 meters. Each time the ball​ bounces, it rebounds to a fraction r of its previous height. Let h Subscript n be the height after the nth bounce. Consider the following values of h 0 and r. Complete parts​ (a) and​ (b) below. a- find the first 4 terms of the sequence of heights(hn)
b- find a general expression for the nth term of the sequence (hn)

h0=20 , r=0.5

Answer 1

Answer: a) first 4 terms would be 10, 5, 2.5, 1.25.

b) $h_n=20(0.5)^{n-1}$

Step-by-step explanation:

Since we have given that

h₀ = 20

r = 0.5

As it is a geometric sequence.

So, hₙ would be

$h_n=h_0r^{n-1}\\\\h_n=20(0.5)^{n-1}$

First 4 terms would be

$h_1=20(0.5)=10\\\\h_2=20(0.5)^2=5\\\\h_3=20(0.5)^3=2.5\\\\h_4=20(0.5)^4=1.25$

Hence, a) first 4 terms would be 10, 5, 2.5, 1.25.

b) $h_n=20(0.5)^{n-1}$