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

Question

Find the third iterate, x_3, of the function f(x) = 3x + 5 for an initial value of x_0 = 1.

Answer 1

Some clarification first --

   Some people start sequences using S₀, and some use S₁.  Looks like you are using S₀.

   The first term is defined by S₀=1.  Subsequent terms are defined by S_n+1=3S_n + 5, or equivalently, S_n=3S_n-1 + 5.

 

This produces the sequence:

       1   8   29   92   281   848   1549    7652   ...

 

O.K., you may select the "third iterate."