Question

A sequence is defined by the recursive function f(n + 1) = f(n) – 2.

If f(1) = 10, what is f(3)?
A.1
B.6
C.8
D.30

Answer 1

To find f(3) for the given sequence, recursively apply the formula f(n + 1) = f(n) - 2. Starting with f(1) = 10, calculate f(2) and then f(3), which results in a value of 6.

Step-by-step explanation:

The question asks for the value of f(3) given a recursive sequence defined by f(n + 1) = f(n) - 2 and an initial value of f(1) = 10. To find f(3), we apply the recursion formula starting from n = 1 and continuing to n = 2, which then allows us to find f(3).

1. Starting with f(1) = 10, we find f(2) by subtracting 2: f(2) = f(1) - 2 = 10 - 2 = 8.
2. To find f(3), we again subtract 2: f(3) = f(2) - 2 = 8 - 2 = 6.

Therefore, the value of f(3) is 6, which corresponds to option B.