Question

If a sequence is defined recursively by f(0) = 3 and f(n+1) = -f(n) + 5 for n greater than or equal to 0, then what is the value of f(2)?

a) 2
b) 3
c) 5
d) 8

Answer 1

To find the value of f(2) in the recursive sequence, we first calculate f(1) using the given recursive formula, then use f(1) to find f(2). The calculated value of f(2) is 3.

Step-by-step explanation:

The student's question is concerned with finding the value of f(2) for a recursively defined sequence with initial condition f(0) = 3 and the recursive step f(n+1) = -f(n) + 5 for n ≥ 0. To find the value of f(2), let's use the recursive definition to determine the first few terms of the sequence:

f(0) = 3, given by the initial condition.f(1) = -f(0) + 5 = -3 + 5 = 2.f(2) = -f(1) + 5 = -2 + 5 = 3.

Therefore, the value of f(2) is 3, which corresponds to option b).