To solve for \( f(2) \) given the recurrence relation:
[tex]\[
\begin{array}{l}
f(1) = -3 \\
f(n) = -5 \cdot f(n-1) - 7
\end{array}
\][/tex]
we need to follow these steps:
1. Identify the value of \( f(1) \):
[tex]\[
f(1) = -3
\][/tex]
2. Use the recurrence relation to find \( f(2) \):
[tex]\[
f(2) = -5 \cdot f(1) - 7
\][/tex]
3. Substitute the value of \( f(1) \) into the equation for \( f(2) \):
[tex]\[
f(2) = -5 \cdot (-3) - 7
\][/tex]
4. Simplify the multiplication:
[tex]\[
f(2) = 15 - 7
\][/tex]
5. Perform the subtraction:
[tex]\[
f(2) = 8
\][/tex]
Thus, the value of \( f(2) \) is:
[tex]\[
f(2) = 8
\][/tex]
