Final Answer:
The correct sequence corresponding to the recursively defined function is Option 2: 0, -1.5, -7.5, -1.75, -5.25.
Step-by-step explanation:
The given recursively defined function generates a sequence of numbers. To find the first five terms, we start with an initial value and apply the recursive rule. Let's denote the terms as a₀, a₁, a₂, a₃, and a₄.
1. Initial Term (a₀): The first term is given as 0 in Option 2.
2. Recursive Rule: The recursive rule seems to be multiplying the previous term by -1.5 and adding a constant term. Applying this rule, we get the following calculations:
- a₁ = 0 * (-1.5) + (-1.5) = -1.5
- a₂ = -1.5 * (-1.5) + (-1.5) = -7.5
- a₃ = -7.5 * (-1.5) + (-1.5) = -1.75
- a₄ = -1.75 * (-1.5) + (-1.5) = -5.25
3. Final Sequence: Putting it all together, the first five terms of the sequence are 0, -1.5, -7.5, -1.75, and -5.25, which matches (Option 2).
In conclusion, by applying the given recursive rule to the initial term, we obtained a sequence that matches the values in Option 2. This confirms that Option 2 accurately represents the first five terms of the sequence generated by the recursively defined function.