Answer:
A)1st term:45
2nd term:48.75
3rd term:49.6875
4th term:49.921875
B) Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)
Step-by-step explanation:
We are given;
h₀ = Initial height of the ball = 30
r = Rebound fraction = 0.25
a) The arithmetic sequence of bouncing balls is given by the following;
Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)
The first term of the sequence is;
S₁ = h₀ + 2h₀r¹
S₁ = 30 + (2 × 30 × 0.25)
S₁ = 45
The second term of the sequence is;
S₂ = h₀ + 2h₀(r¹+r²)
S₂ = 30 + (2 × 30 × (0.25 + 0.25²)) = 48.75
The third term of the sequence is;
S₃ = h₀ + 2h₀(r¹ + r² + r³) = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³)) = 49.6875
S₄ = h₀ + 2h₀(r¹ + r² + r³ + r⁴)
S₄ = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³ + 0.25⁴)) = 49.921875
B) The general expression for the nth term of the sequence is;
Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)
