The question appears to involve checking whether a recursively defined sequence matches an explicit formula. Based on the image, the marked question involves:

$a_1 = 0,$ $a_n = 4a_{n-1} + 3, \text{ for } n \geq 2.$

We need to determine if this recursive definition satisfies the explicit formula $a_n = 4^n - 3$.

Solution:

1. Base case:
   • For $n = 1$, the explicit formula gives $a_1 = 4^1 - 3 = 4 - 3 = 1$, but the recursive definition says $a_1 = 0$.
   • Hence, the recursive definition does not match the explicit formula starting from $n = 1$.

The recursive definition fails to satisfy the explicit formula from the very first term, so they are not equivalent.

Would you like more details or further explanations?

Here are some related questions you might find interesting:

1. How do you prove if a recursive formula matches an explicit formula?
2. What are the typical steps to convert recursive sequences into explicit ones?
3. How do initial conditions affect the general solution of recursive sequences?
4. Can recursive sequences be solved for large $n$ using approximation techniques?
5. What role does induction play in verifying explicit formulas?

Tip: Always compare the base case when verifying recursive sequences against explicit formulas!