To find [tex]\( f(5) \)[/tex] in the sequence defined by the recursive formula [tex]\( f(n+1) = f(n) - 2 \)[/tex] with the initial condition [tex]\( f(1) = 18 \)[/tex], let's proceed step-by-step:
1. Initial condition:
[tex]\[
f(1) = 18
\][/tex]
2. Calculate [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = f(1) - 2 = 18 - 2 = 16
\][/tex]
3. Calculate [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = f(2) - 2 = 16 - 2 = 14
\][/tex]
4. Calculate [tex]\( f(4) \)[/tex]:
[tex]\[
f(4) = f(3) - 2 = 14 - 2 = 12
\][/tex]
5. Calculate [tex]\( f(5) \)[/tex]:
[tex]\[
f(5) = f(4) - 2 = 12 - 2 = 10
\][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\( \boxed{10} \)[/tex].
