Sure, let's work through this step-by-step.
1. Initial Condition:
We are given that [tex]\( f(1) = 1 \)[/tex].
2. First Iteration:
We need to find [tex]\( f(2) \)[/tex] using the given recursive function [tex]\( f(n+1) = -10 f(n) \)[/tex].
So, for [tex]\( n = 1 \)[/tex]:
[tex]\[
f(2) = -10 \cdot f(1)
\][/tex]
Substituting [tex]\( f(1) = 1 \)[/tex]:
[tex]\[
f(2) = -10 \cdot 1 = -10
\][/tex]
3. Second Iteration:
Next, we need to find [tex]\( f(3) \)[/tex] using the recursive function [tex]\( f(n+1) = -10 f(n) \)[/tex].
So, for [tex]\( n = 2 \)[/tex]:
[tex]\[
f(3) = -10 \cdot f(2)
\][/tex]
Substituting [tex]\( f(2) = -10 \)[/tex]:
[tex]\[
f(3) = -10 \cdot (-10) = 100
\][/tex]
Therefore, [tex]\( f(3) = 100 \)[/tex].
