Question

Consider the recursively defined function below. Create the first five terms of the sequence defined by the given function.

1) 1.5, 0, -1.5, -7.5, -1.75
2) 0, -1.5, -7.5, -1.75, -5.25
3) 1.5, 0, -1.5, -7.5, -1.75, -5.25
4) 0, -1.5, -7.5, -1.75, -5.25, 1.75

Answer 1

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.