1. The problem involves interpreting expressions related to Fibonacci numbers and matching them to verbal descriptions. 2. Recall the Fibonacci sequence $F_n$ is defined as $F_0=0$, $F_1=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\geq 2$. 3. We analyze the expressions given: - $F_{3N} - 2$ means "two less than the $(3N)$th Fibonacci number". - $3F_{N} - 2$ means "three times the $N$th Fibonacci number, then subtract 2". 4. From the options in part (b), the correct verbal description for $F_{3N} - 2$ is: **A. two less than (3N)th Fibonacci number** 5. For $3F_{N} - 2$, the correct verbal description is: **G. three less than two times the Nth Fibonacci number** is incorrect because it implies $2F_N - 3$. **E. two less than three times the Nth Fibonacci number** matches $3F_N - 2$. 6. Therefore, the correct matches are: - $F_{3N} - 2$ corresponds to option A. - $3F_N - 2$ corresponds to option E. Final answer: - For $F_{3N} - 2$: A. two less than (3N)th Fibonacci number - For $3F_N - 2$: E. two less than three times the Nth Fibonacci number