3. Proof Techniques II

Recursive Definitions — Quiz

Test your understanding of recursive definitions with 5 practice questions.

Practice Questions

Question 1

In the recursive definition of the factorial function, which part is the base case?

Question 2

For the recursive sequence $a_1=2$ and $a_n=a_{n-1}+3$ for $n\ge 2$, what is $a_3$?

Question 3

What is required in a recursive definition of a sequence so that later terms can be determined uniquely?

Question 4

For $f(0)=5$ and $f(n)=f(n-1)-1$ for $n\ge 1$, what is $f(2)$?

Question 5

Which statement best describes the recursive step in a recursive definition?