Question

The first four terms of a sequence are shown below:

9, 5, 1, -3
Which of the following functions best defines this sequence?
f(1) = 9, f(n + 1) = f(n) - 4; for n ≥ 1.
f(1) = 9, f(n + 1) = f(n) + 4; for n ≥ 1.
f(1) = 9, f(n + 1) = f(n) - 5; for n ≥ 1.
f(1) = 9, f(n + 1) = f(n) + 5; for n ≥ 1.

Answer 1

The function that best defines the sequence 9, 5, 1, -3 is f(1) = 9, f(n + 1) = f(n) - 4; for n ≥ 1, where each term is 4 less than the previous term.

Step-by-step explanation:

The sequence given is 9, 5, 1, -3. To find the function that defines this sequence, we look for a pattern in the differences between successive terms. The difference between the first and second terms is 5 - 9 = -4, between the second and third terms is 1 - 5 = -4, and between the third and fourth terms is -3 - 1 = -4. This shows us that each term is 4 less than the previous term, which means we are subtracting 4 each time to get the next term.

Therefore, the function that defines this sequence starts with f(1) = 9 and for each subsequent term, is f(n + 1) = f(n) - 4; for n ≥ 1. This function correctly shows that each term is 4 less than the term before it, thus representing the given sequence accurately.