Iterate Please help! :)

Question

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

Answer 1

Your initial value is x₀ = 1.

 

 

 

To find x₁, put x = x₀ = 1 into the function:

 

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

 

 

 

Now, find x₂ by putting x = x₁ = 8 into the function:

 

x₂ = f(8) = 3(8) + 5 = 24 + 5 = 29

 

 

 

Finally, iterate one more time using x = x₂ = 29:

 

x₃ = f(29) = 3(29) + 5 = 87 + 5 = 92