Worksheet: Iterated Functions

In this worksheet, we will practice iterating a function to recursively generate a sequence.

Q1:

Given an initial value 𝑥 0 , we can iterate a function using the recursive formula 𝑥 = 𝑓 ( 𝑥 ) 𝑖 𝑖 1 .

Find 𝑥 3 given the function 𝑓 ( 𝑥 ) = 3 𝑥 2 with initial value 𝑥 = 2 0 .

Q2:

We can define a sequence 𝑥 , 𝑥 , 𝑥 , 0 1 2 using the recursive formula 𝑥 = 𝑓 ( 𝑥 ) 𝑖 𝑖 1 for some function 𝑓 and initial value 𝑥 0 .

Write the first 5 terms of the sequence generated by 𝑓 ( 𝑥 ) = 8 3 𝑥 𝑖 𝑖 1 , 𝑥 = 1 1 0 .

  • A 1 1 , 2 5 , 8 3 , 2 4 1 , 7 3 1
  • B 1 1 , 8 , 1 6 , 5 6 , 1 6 0
  • C 1 1 , 4 1 , 1 1 5 , 3 5 3 , 1 0 5 1
  • D 1 1 , 4 1 , 1 1 5 , 3 5 3 , 1 0 5 1
  • E 1 1 , 4 1 , 1 1 5 , 3 3 7 , 1 0 1 9

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