Final answer:
The correct sequence matching both the recursive formula aₙ = aₙ−1 + 4, a₁ = −9 and the explicit formula aₙ = 4n − 13 is b) -9, -5, -1, 3, …. This sequence was determined by applying both formulas to the first few terms.
Step-by-step explanation:
To find the sequence that corresponds to the given recursive formula and explicit formula, we start by looking at the first term provided, a1 = -9.
Using the recursive formula an = an-1 + 4, and starting with a1 = -9:
- a2 = a1 + 4 = -9 + 4 = -5
- a3 = a2 + 4 = -5 + 4 = -1
- a4 = a3 + 4 = -1 + 4 = 3
This sequence matches option b) -9, -5, -1, 3, …
To verify with the explicit formula, an = 4n - 13:
- a1 = 4(1) - 13 = -9
- a2 = 4(2) - 13 = -5
- a3 = 4(3) - 13 = -1
- a4 = 4(4) - 13 = 3
Thus, the correct sequence is b) -9, -5, -1, 3, …, which follows both the recursive and explicit formulas given.