Find the third iterate, x3, of the function f(x) = 3x + 5 for an initial value of x0 = 1.

Question

Find the third iterate, x3, of the function f(x) = 3x + 5 for an initial value of x0 = 1.

Answer 1

x₀ = 1

x₁ = f(x₀) = f(1) = 3(1) + 5 = 3 + 5 = 8

x₂ = f(x₁) = f(8) = 3(8) + 5 = 24 + 5 = 29

x₃ = f(x₂) = f(29) = 3(29) + 5 = 87 + 5 = 92