Question
A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?
Answers
GPT-4o mini
To find \( f(5) \) from the given recursive formula \( f(n + 1) = f(n) - 2 \) with the initial condition \( f(1) = 18 \), we will calculate the values step by step.
1. **Find \( f(2) \)**:
\[
f(2) = f(1) - 2 = 18 - 2 = 16
\]
2. **Find \( f(3) \)**:
\[
f(3) = f(2) - 2 = 16 - 2 = 14
\]
3. **Find \( f(4) \)**:
\[
f(4) = f(3) - 2 = 14 - 2 = 12
\]
4. **Find \( f(5) \)**:
\[
f(5) = f(4) - 2 = 12 - 2 = 10
\]
Thus, the value of \( f(5) \) is \(\boxed{10}\).
1. **Find \( f(2) \)**:
\[
f(2) = f(1) - 2 = 18 - 2 = 16
\]
2. **Find \( f(3) \)**:
\[
f(3) = f(2) - 2 = 16 - 2 = 14
\]
3. **Find \( f(4) \)**:
\[
f(4) = f(3) - 2 = 14 - 2 = 12
\]
4. **Find \( f(5) \)**:
\[
f(5) = f(4) - 2 = 12 - 2 = 10
\]
Thus, the value of \( f(5) \) is \(\boxed{10}\).