To find [tex]\( f(6) \)[/tex] in the given sequence defined recursively by [tex]\( f(n+1) = f(n) - 8 \)[/tex] with the initial value [tex]\( f(1) = 100 \)[/tex], follow these steps:
1. Start with the initial value:
[tex]\[ f(1) = 100 \][/tex]
2. Use the recurrence relation to find the subsequent terms:
[tex]\[
f(2) = f(1) - 8 = 100 - 8 = 92
\][/tex]
[tex]\[
f(3) = f(2) - 8 = 92 - 8 = 84
\][/tex]
[tex]\[
f(4) = f(3) - 8 = 84 - 8 = 76
\][/tex]
[tex]\[
f(5) = f(4) - 8 = 76 - 8 = 68
\][/tex]
[tex]\[
f(6) = f(5) - 8 = 68 - 8 = 60
\][/tex]
So, the value of [tex]\( f(6) \)[/tex] is [tex]\( 60 \)[/tex].
Thus, the correct answer is 60.
