Answer:
a) 40, 50, 55, 57.5
b)
Step-by-step explanation:
h₀ = Initial height of the ball =20
r = Rebound fraction = 0.5
a) The series of bouncing balls is given by
Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)
S₁=h₀+2h₀r¹=20+2×20×0.5=40
S₂=h₀+2h₀(r¹+r²)=20+2×20×(0.5+0.5²)=50
S₃=h₀+2h₀(r¹+r²+r³)=20+2×20×(0.5+0.5²+0.5³)=55
S₄=h₀+2h₀(r¹+r²+r³+r⁴)=20+2×20×(0.5+0.5²+0.5³+0.5⁴)=57.5
b) General expression for the nth term of the sequence