Question

If a sequence is defined recursively by F(0) = 3 and F(n + 1) = -F(n) + 5 for n ≥ 0, what is the value of F(2)?

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

Answer 1

Using the recursive formula, F(2) is calculated by first finding F(1), which is 2. Then, applying the formula again, F(2) is found to be 3.the correct answer is choice b) 3.

Step-by-step explanation:

If a sequence is defined recursively by F(0) = 3 and F(n + 1) = -F(n) + 5 for n ≥ 0, to find the value of F(2), we need to sequentially compute terms until we reach F(2). First, we find F(1) by applying the recursive formula to F(0):

F(1) = -F(0) + 5 = -3 + 5 = 2.

Now, to calculate F(2), we apply the recursive formula again using F(1):

F(2) = -F(1) + 5 = -2 + 5 = 3.

Therefore, the value of F(2) is 3, which means the correct answer is choice b) 3.