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Fill in the blank in the following sequence:
[tex]\[
\begin{array}{l}
\left\{
\begin{array}{l}
f(1) = -3 \\
f(n) = -5 \cdot f(n-1) - 7
\end{array}
\right. \\
f(2) = \square
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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